Deputies say Alfred Tapia, 34, is considered armed and dangerous.
Tapia's wave of violence began on Dec. 3. Officials say Tapia nearly stabbed his uncle to death on the 8700 block of Olympic Way in Pico Rivera.
Two days later, Tapia allegedly attacked a friend with a hammer and a knife on the 10500 block of Nashville Avenue in the unincorporated area of Whittier.
Then, on Dec. 6, authorities say Tapia seriously attacked his aunt with a knife, leaving her with serious injuries.
Deputies say many of Tapia's family members are concerned about their safety, and authorities want to stop this attempted-murder suspect before he strikes again.
"Well there is an obviously ingrained tendency toward violence which has been apparent by Mr. Tapia, and as far as specific motives to each and individual assault, investigators are still looking into that. So we haven't determined a specific motive as to each specific assault," said Lt. Martin Rodriguez with the Los Angeles County Sheriff's Department.
Tapia has a tattoo of the letters "CS" on his left elbow and the name "Kathy" on his chest.
Tapia was last seen driving a 2003 black Lexus sedan with California license plate number 5CFB492. If you have any information about Tapia's whereabouts, you're urged to call Los Angeles Regional Crime Stoppers at (800) 222-TIPS or (800) 222-8477.