The new charge means that if Daniel Chase McKibben, 36, is convicted of first-degree murder, he would face life in prison without the possibility of parole.
The victim is Heidi Green, 59, who was found dead in a home in the 5000 block of Niagara Avenue near the OB Pier on May 1. Authorities have not said how she died and the facts of the case have not been discussed in court.
McKibben appeared Monday in jail clothes before San Diego Superior Court Judge Michael Smyth and he waived his right to have speedy court proceedings.
He has pleaded not guilty to all charges and remains in jail without bail.
A family member called police asking for a welfare check on Green and police found her deceased.
McKibben turned up at a home in La Mesa the next day. A resident there called La Mesa Police, saying McKibben would not leave and was trespassing in the 7900 block of Rainey Street.
Police showed up at 9:15 a.m. May 2 and discovered that McKibben allegedly was armed with a knife. An officer shot him twice in the shoulder and hand.
McKibben was taken to a hospital and was arraigned in his hospital bed.