Voters could decide whether to limit the governor and lieutenant governor to two terms during their lifetimes.
The state House approved the constitutional amendment Tuesday.
Rep. Bert Jones, a Rockingham County Republican, said during an earlier committee hearing that House Bill 105 would apply to all elected governors or lieutenant governors – past, present and future.
The state constitution restricts them to two consecutive terms, but allows them to run for election again after taking a term off from office.
Some lawmakers raised concerns about how that would affect someone who would be appointed to the office instead of being elected. Jones amended the bill to clarify that partial terms, or terms that someone was appointed to, would not count toward the term limit.
The bill now goes to the Senate. If approved in the legislature, it would go to a statewide vote in November 2018.
There are no term limits for members of the legislature. A House committee this month rejected a term-limit proposal for lawmakers that also would have increased the length of terms.