The Internal Revenue Service is investigating longtime National Rifle Association CEO Wayne LaPierre for possible criminal tax fraud related to his personal taxes, according to people familiar with the matter.

Mr. LaPierre was paid $2.2 million by the NRA in 2018, the most recent year available, the nonprofit group’s public filings show. His total reported pay from 2014 to 2018 was $11.2 million.

In…