A young Korean tourist has fought off a man who slipped into her bed after sneaking into a Melbourne apartment for backpackers.



The man had gained access to the St Kilda apartment block through an unlocked door at 4am last Saturday and wandered around the building until he found a bedroom where four tourists, all women in their early 20s, were sleeping.



Police say the man then took his jumper off, pulled back the blankets on one of the beds and tried to get in bed with the sleeping woman.



She was stirred awake by the man grabbing at her arm and leg, and she began kicking him in a bid to chase him away.



The three other women in the room were woken by her screams, and one of them confronted the man and followed him out of the Acland Street building.



But the man returned minutes later through another unlocked door, approached another woman in a bathroom and began following her.



She only got away by pushing her own door shut and locking it, police said.



Detective Senior Constable Lauren Halliwell says the women are all very shaken up over series of late-night incidents.



"It's very worrying when young females can't feel safe in their own home," she said.



The woman confronted in her bed is touring Australia on a working holiday, while her housemates are all from Europe.



Police say the intruder needs to be caught quickly.



"It's concerning as he's very casual about his actions," Senior Detective Halliwell said.



The man is described as being African in appearance, in his mid-20s, with a shaved head. He was wearing a grey hooded top with a “Compton” logo, a green and white long-sleeved shirt and dark pants.



Police have released CCTV footage of the man slowly walking around the apartment.



Anyone with information is asked to phone Crime Stoppers on 1800 333 000.