FAIRFAX, Va.—To succeed in his insurgent campaign to become Virginia’s next governor, Tom Perriello first has to convince Democratic primary voters he really is an insurgent.

To win what is expected to be a low-turnout primary June 13, the former one-term congressman aims to expand the state’s Democratic electorate by tens of thousands of new voters—the sort of people who emerged to back Barack Obama and Bernie Sanders in the last two presidential primaries. He is campaigning this week at college campuses and held a rally last week with Mr. Sanders at George Mason University.

“We’re hoping it’s an electorate that reflects the full Democratic Party in the state as a whole,” Mr. Perriello said in an interview Tuesday. “People appreciate a candidate who is not just looking at the existing party but going out to where the energy is now.”

But unlike Messrs. Obama and Sanders, the 42-year-old Mr. Perriello doesn’t have a lifetime of unblemished progressive activism to harness in wooing the party’s re-energized left.

Before losing his Charlottesville, Va.-based House seat in the 2010 tea-party wave, he voted for the Affordable Care Act, but also cast votes that angered abortion-rights activists.