Martínez’ family moved to Los Angeles, California when he was young and he attended public schools in Los Angeles. In 1949 he graduated from Roosevelt High School. From 1947 to 1950 he served in the U.S. Marine Corps, achieving the rank of private first class. In 1956 he received a certificate of competence from the Los Angeles Trade Technical School.

For the next fifteen years he owned and operated a custom furniture upholstery company, and worked as a building contractor. He began his political career in 1971 when he became a member of the Monterey Park Planning Committee, and served until 1974 when he was elected to the Monterey Park City Council. He served until 1980, including two terms as mayor in 1974 and 1980. In the 1980 Democratic primary, Martínez defeated incumbent Jack R. Fenton and was elected to the California State Assembly.

In 1982 Martínez won the special election to fill the vacancy in the U.S. House of Representatives caused by the resignation of George E. Danielson, and was reelected seven times.

In his first term in Congress he was assigned to the Education and Labor Committee. In the 99th Congress (1985-87) he chaired the Subcommittee on Employment Opportunities. In 1991 he became the Chairman of the Human Resources Subcommittee. In 1992 Martínez was named to the Foreign Affairs Committee, and served on the Subcommittee on International Security, International Organizations and Human Rights.

In 2000, Martínez was defeated in the primary election by Hilda Solís. Solís claimed he was out of touch with his district when he voted to ban partial-birth abortion and opposed gun control. On July 27, 2000, Martínez switched to the Republican Party and claimed that the Democrats had abandoned him. Martínez attempted to garner more support from Latino voters on his Republican ticket but he was ultimately unsuccessful in the 2000 election. His term in Congress ended on January 3, 2001 at the end of the 106th Congress.