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.
