LONDON—A self-described "soldier of Allah" who killed a British serviceman in a London street has launched a legal bid to overturn his murder conviction.

The Judicial Office said Thursday that 29-year-old Michael Adebolajo had submitted an application to appeal.

Adebolajo and another man, Michael Adebowale, were convicted in December of murdering Fusilier Lee Rigby, who was run down by a car and then stabbed near his London barracks in May.

Adebolajo admitted the killing but said it was not murder because he was a "soldier of Allah" engaged in a war.

The men have not yet been sentenced. The judge said he would await a ruling in an appeals court case on the use of life sentences without parole, due later this year.