Born in 1935 in New York, the son of a janitor, Moses attended Stuyvesant High School for gifted students, graduating in 1952 and elected senior class president and captain of the baseball team . He graduated from Hamilton College in upstate New York in 1956, and received a master's degree in philosophy from Harvard in 1957.

Dropping out of graduate school upon his mother's death, Moses began working as a math teacher at the private Horace Mann School in New York. In 1960, when Southern black students began sit-ins in the civil rights struggle, Moses joined the movement and became a field organizer with the Student Non-violent Coordinating Committee (SNCC). He spent the next four years in the South, becoming one of the most important figures in the movement for his efforts to turn the emphasis from sit-ins and freedom rides to voter registration and education.

At the time of the SNCC activities in Mississippi, less than 5% of the black population was registered to vote. There was a literacy requirement that effectively shut out many potential voters. Moses and SNCC organized "freedom schools" to teach people how to pass the literacy test. In 1964 a drive to recruit white students from the North to come to Mississippi and the South and help with the literacy and voter registration projects netted 1000 volunteers in what became known as "Freedom Summer."

After his civil rights activities, Moses was drafted in 1966 and fled to Canada. Moses eventually moved to Tanzania and spent eight years teaching mathematics. Returning to the United States and settling in Cambridge, Massachusetts, Moses resumed work on his doctorate. Having begun tutoring his daughter in math due to his unhappiness with the quality of instruction she was receiving, Moses accepted a volunteer position as a math tutor in the Cambridge public school system.

Bob Moses received a 1982 MacArthur Foundation grant, called the "genius" grant, and used the funds from the five-year grant to start the Algebra Project to teach "mathematical literacy" to inner-city and rural children to prepare them for more advanced math. His concern was the evidence that tracking of students for math placement was being done along racial lines, with many students of color being shifted into the less-advanced track. He also saw a trend of high-achieving students of color being influenced by their peers into being ashamed of their intelligence. The Algebra Project uses real-world examples to teach children to think in mathematical terms and relate math to the world around them.

More than 40,000 students have been helped to master fundamental algebraic skills in 25 cities and the number of school systems is growing. In 1992, Moses started an off-shoot, the Delta Algebra Project, in Mississippi. Bob Moses was honored for his work by the Mississippi State Senate in 2000 with a special resolution.