Two of the incidents happened while women were walking along Magnolia Avenue between Hollywood Way and Buena Vista Street, an area lined with shops and restaurants.
The other happened on Buena Vista Street and Chandler Boulevard.
"The circumstances seem to be women of various ages walking through the city, either citizens or visitors to our city," said Sgt. John Pfrommer of the Burbank Police Department.
In each of the instances, the man wore a white shirt, a tie and dress pants.
He's described as either white or Hispanic, between the ages of 35 and 40, 6-feet tall, with a shaved or bald head.
Anyone with information is asked to call Burbank police at (818) 238-3000.