McDowell followed up his opening 69 with a 70 at the Riviera Country Club in California.
However, 121 players still to finish their rounds because wind and rain led to PGA officials halting play.
Sam Saunders of the US is tied on seven under with Venezuelan Jhonattan Vegas at the top of the leaderboard.
Saunders has yet to start his second round while Vegas has played 14.
McDowell, 37, was one of only 24 players able to complete their second rounds as a storm battered the course.
A huge limb from a eucalyptus tree fell near the third hole and with heavy rain falling play was called off.
Northern Ireland's Graeme McDowell posted another solid round at the Genesis Open to be three under par for the weather-hit tournament.