In the 1920s, State Highway 337 followed today's Route 162.

The streets that became modern Route 337 were originally city-maintained. In 1960, the state Committee to Reclassify All Public Roads recommended adding the following roads, totaling 4.94 miles, to the state highway system:

• Townsend Avenue, from US 1 in New Haven to the East Haven town line
• South End Road (continuation of Townsend Avenue) to Silver Sands Road in East Haven
• Silver Sands Road to Short Beach Road (Route 142)

In 1963, these roads became a westward extension of Route 142. In 1969, however, the state reverted Route 142 back to its 1962 alignment and the new roads became unsigned SR 704.

On Sept. 15, 1987, SR 704 became Route 337.

In 1997, a small change was made to Route 337's eastern end: instead of following Silver Sands Road to Short Beach Road, it now turns north on Coe Avenue to connect with Route 142. The change decreased its length by 0.03 miles, to 4.91 miles.