Rose, the son of a wealthy leather tanner, was born in Warsaw, Poland. After secondary school, Rose immigrated to the United States, having been denied a Polish university education because he was Jewish. However, the outbreak of the First World War forced Rose to abandon professional aspirations and take a job as a millinery worker; in 1914 he joined the Cloth Hat, Cap, and Millinery Workers' International Union (CHCMW) and became interested in organized labor. In 1918, Rose joined the British Army, and upon returning to America in 1920 resumed union organizing activities. He worked his way through union leadership and was elected president of the Hatters' Union in 1950, where Rose sought to root out Communist and gangster influence from unions.
In 1936, Rose assisted in founding of the American Labor Party. Because the communists acquired influence in the ALP, in 1944 Rose, along with David Dubinsky, Ben Davidson, and others founded the Liberal Party of New York. Rose became its vice-chairperson. Under Rose's leadership, the Liberal Party was quite influential in New York politics and somewhat influential in national politics, exercising power by endorsing Democratic and occasionally, liberal Republican candidates. In 1966 Rose successfully lobbied Senator Robert F. Kennedy to campaign on behalf of judge Samuel Silverman to clean up corruption from the surrogate court.
Rose was one of the most brilliant political strategists of the 20th century. Perhaps his greatest triumph was in the New York City mayoral election of 1969. John V. Lindsay was elected mayor as a fusion candidate (Republican-Liberal) in 1965, but was denied the Republican nomination in 1969. Alex Rose directed Lindsay's reelection campaign in 1969 as the Liberal candidate against both Democratic and Republican opponents so successfully that he not only was reelected, but he brought on his coat-tails enough Liberal councilmen to displace the Republicans as minority party in the City Council.
After Rose's death in 1976, leadership of the Liberal Party passed to Raymond B. Harding, who also exerted a considerable amount of influence in New York State politics until the party lost its ballot line in 2002.
One block of W. 186th Street in Manhattan (between Chittenden Avenue & Cabrini Boulevard) is named "Alex Rose Place."
- Chris McNickle (1993). To be Mayor of New York: Ethnic Politics in the City. Columbia UP. pp. 45–57.
- Jews in American Politics by Louis Sandy Maisel, Ira N. Forman, Donald Altschiller, and Charles Walker Bassett
- Robert Kennedy and His Times by Arthur M. Schlesinger, Jr.
- New York Day By Day; A Place for Alex Rose
- Liberal Party of New York State Records