A murderer who strangled a Brisbane mother before stealing her money and trying to cover his tracks has been sentenced to life imprisonment.

Robert Graham Thomas represented himself before being sentenced in the Brisbane Supreme Court on Thursday for the 2015 murder of Danielle Miller.

Mother-of-two Danielle Miller was murdered in her home. Credit:AAP

Ms Miller, who had been in a casual sexual relationship with Thomas, was found by police lying face up alongside a broken fan and a clump of her own hair in her Greenslopes home in Brisbane's south-east.

Thomas' trial heard he tried to cover up his crime by throwing clothing Ms Miller had worn before her death into a bin at a building site at the property next door.