The attacks happened Sunday around 4:30 a.m. in two locations in downtown Los Angeles.
Police say the suspect approached sleeping homeless men and beat them repeatedly on the head and shoulders with a baseball bat, then ransacked their pockets and belongings to rob them.
"These are human beings. They simply don't have shelter. They don't have a roof over their heads. So for someone to attack them whilst they're sleeping? It breaks my heart," said Kitty Davis-Walker, with the Union Rescue Mission.
One of the victims was found unconscious in the 700 block of Wilshire Boulevard and two of them were found in the area of 5th Street between Flower and Figueroa.
The suspect is also believed to be homeless, based on his appearance and surveillance video that shows him rummaging through trash as he walked around the area.
"This is a FEMA-like emergency, and we can't continue like this, but we all can do something," Davis-Walker said.
She's urging people to call elected officials to push for action and support shelters that are outpaced by the people experiencing homelessness.
The suspect was described as a man in his 30s or 40s with medium height and build, dark bushy hair, wearing a blue hat, gray sweatshirt, black shorts and bright white tennis shoes. One of his more distinctive traits is a unique gait caused by outwardly bowed legs, police said.
His victims remained in critical condition with severe head trauma and have not been conscious since the attacks, police said.
Anyone with information is asked to contact LAPD Robbery-Homicide Division Detectives Daryn Dupree, David Holmes or Laura Evens at (213)486-6860, or the Real Time Analysis and Critical Response Division at (213)484-6700.
Anonymous tips can be provided to LA Crime Stoppers at (800)222-TIPS.