Alex Reuben McEwan "just felt like" killing Eunji Ban, but he doesn't believe he's her murderer.
McEwan has pleaded not guilty to murdering the South Korean woman in Brisbane's CBD in November 2013, but guilty to her manslaughter.
His ability to control his actions was impaired by his schizophrenia, his lawyer argues.
But the Crown did not accept his plea to the lesser charge, telling his trial that he intended to kill her.
"He told police he went out looking for someone to kill," crown prosecutor David Meredith told Brisbane Supreme Court in opening submissions on Monday.
Ms Ban, 22, was found dead in Wickham Park in the early hours of November 24, 2013 after she was allegedly repeatedly punched by McEwan, then 19, while walking to her cleaning job.
Her head injuries were so severe they caused her to drown in her own blood, the court heard.
McEwan's friend Hayden Buchanan took a call from him at 5am, about an hour after he killed Ms Ban.
"(He said) 'I've just killed someone. I just went out and bashed someone. I just went for a walk and killed someone'," Mr Buchanan testified on Monday.
"'I just felt like it'."
McEwan, from Brisbane, was unable to offer an explanation, the court heard.
He then suggested he and Buchanan should get "one last pub meal, a big juicy steak" before he goes to jail.
"You'll need to look beyond that crime and into the mind of the killer," defence lawyer John Allen QC told the jury.
"Mr McEwan's out-of-character, extreme violence was caused by his mental illness."
McEwan's friends testified violence was out of his character.
He was not blind drunk as he socialised with friends at his Spring Hill unit on the night before the alleged murder, according to those who gave evidence on Monday, but may have smoked a small amount of marijuana.
Earlier that night, he said "why does this always happen to me" after leaving his bank card at a driving range, and was later asked to leave a party in Tarragindi after knocking over a tarp, the court heard.
Ms Ban had set out from a Roma Street Parklands unit about 4am via a walkway leading to Albert Street, the court heard.
After killing her, McEwan allegedly dragged her body up a flight of stairs to Wickham Park and left her by a tree, leaving a trail of blood.
A hospitality worker saw what appeared to be someone pulling something up stairs at Wickham Park before discovering Ms Ban's body and calling triple-zero shortly before 5am, the court heard.
The trial continues on Tuesday.