Because of the grave dangers to the future of mankind in the nuclear testing policies of the three leading nations of the world, we call upon men everywhere to consider non-violent direct action against the evil of nuclear tests.” These were the opening words of the call to Non-Violent Action Against Nuclear Weapons, an ad hoc committee organized in May 1957 by Quaker pacifist Lawrence Scott, to protest against nuclear tests in Las Vegas, Nevada. In September 1958, this ad hoc committee reorganized as a permanent committee, the Committee for Nonviolent Action, sponsored at first by the Fellowship for Reconciliation, Friends Peace Committee of Philadelphia Yearly Meeting, War Resisters League, and Women's International League for Peace and Freedom. Early leaders of both NVAANW and CNVA, besides Scott, included A.J. Muste, George Willoughby, Lyle Tatum, Bayard Rustin, Ralph diGia, Theodore Olson, and Albert Bigelow. Headquartered at first in Philadelphia, CNVA soon moved to New York City.

CNVA was one of the first American peace groups to focus on nonviolent direct action including civil disobedience. Its purpose of organizing imaginative and dramatic protest demonstrations on both land and sea attracted radical pacifists and called the attention of the American public to the atrocities of nuclear warfare. CNVA was not a membership organization but rather requested those interested to participate in its demonstrations and to commit themselves to the discipline of nonviolence.

The Committee itself had approximately 65 members. Decisions were made by its Executive Committee. Regional offices soon sprang up elsewhere in the United States, the most prominent being New England CNVA in Voluntown, Connecticut, under the leadership of Marjorie and Robert Swann and CNVA West in San Francisco, California.

CNVA's first protest action was a vigil held outside the atomic weapons test grounds in Las Vegas, Nevada, in 1957. The following year, the Golden Rule set sail for the South Pacific test area but its crew was stopped and arrested in Honolulu. Earle and Barbara Reynolds continued the effort aboard the Phoenix and successfully entered the test waters. CNVA sponsored Omaha Action in 1959 to protest construction of intercontinental ballistic missiles, and, in 1960, Polaris Action began, coordinated by NECNVA and aimed against the missile-carrying Polaris submarine being constructed in New London. In each and indeed almost every CNVA demonstration, its people were arrested and jailed, submitting peacefully to the indignities and attacks from irate police and public. These events made news headlines everywhere, focusing national attention on them.

Two of the largest CNVA projects were the San Francisco to Moscow Walk for Peace and later, the Quebec-Washington-Guantanamo Walk for Peace. The first event began when walkers left San Francisco in December 1960 and ended in October 1961, 6000 miles later, in Moscow, after CNVA marchers called on governments of all nations to disarm. The Quebec Walk began in 1963 with feeder walks strengthening its numbers. Civil rights became a major issue when walkers were beaten and jailed in Atlanta, Georgia. Because of a U.S. ban on travel to Cuba, the marchers were unable to leave Miami.

In the second half of its existence, additional CNVA leadership was provided by Neil Haworth as national secretary and Eric Weinberger as Field Secretary. In the middle 1960s, CNVA efforts began to focus on Vietnam. A.J. Muste, Brad Lyttle, and Barbara Deming were sent to Saigon but were deported for picketing the United States Embassy. A War Tax Protest with phony Thoreau Money was instituted in 1966. in addition to the organizations that initially sponsored it, CNVA allied its resources with other American peace groups, including CCCO, SANE, the Catholic Peace Fellowship, Congress of Racial Equality, the New York Fifth Avenue Vietnam Peace Parade Committee, the Peacemakers, and Turn Toward Peace. CNVA had its own periodicals including CNVA Bulletin and Polaris Action Bulletin, and worked on WIN magazine begun in 1966 by its affiliate, the New York Workshop in Nonviolence.

As other American peace groups adopted CNVA's methods of dramatic and nonviolent demonstrations, its own numbers and support waned. The death in 1967 of Muste, who had been national chairman since 1959, was another blow, and, in the fall of 1967, CNVA voted to merge with the War Resisters League, which became reality in January 1968.