Henry was born in Chicago, Illinois and graduated from Pasadena High School, Pasadena, California, in 1959. He received a B.A. from Wheaton College, Wheaton, Illinois in 1963. Henry was a Peace Corps volunteer in Liberia and Ethiopia from 1963 to 1965. He earned a MA from Duke University, Durham, North Carolina in 1968, a Ph.D. from Duke in 1970 and was professor of political science at Calvin College in Grand Rapids, Michigan from 1970 to 1978.
While at Calvin College, Henry was a member of the Michigan State Board of Education from 1975 to 1978. He left the college to serve in the Michigan State House of Representatives from 1979 to 1982. He served in the Michigan State Senate from 1983 to 1984. In 1984, Henry was elected as a Republican from Michigan's 5th congressional district to the United States House of Representatives for the 99th and to the four succeeding Congresses. After redistricting following the 1990 Census, he was elected from Michigan's 3rd congressional district in 1992. Henry served in Congress from January 3, 1985, until his death (due to a brain tumor) in Grand Rapids, Michigan. He is interred at Woodlawn Cemetery in Grand Rapids. He was succeeded in Congress by Vernon James Ehlers.
Calvin College established The Paul B. Henry Institute for the Study of Christianity and Politics in 1997 to continue the work of integrating Christian faith and politics advanced by its namesake.
Grand Valley State University's Allendale Campus has a building called Henry Hall, part of the Life Sciences Complex of buildings, which consists of Loutit Lecture Halls, Henry Hall, Student Services Building, and Padnos Hall of Science.