Tsarnaev was found guilty in April of killing Krystale Campbell, 29, Martin Richard, 8, and Lingzi Lu, 23 in the bombing and later fatally shooting MIT Police Officer Sean Collier.
He was given six death penalty sentences.
Everyone who is sentenced to death in a federal court is automatically granted an appeal. According to court documents, Tsarnaev's lawyers are seeking a new judgement on each of his 30 convictions and his six death sentences.
The motion cites "evidentiary insufficiency" as the reason for a new trial.
Tsarnaev's motion comes less than two weeks after he stood up in court to apologize for the two bombs, which also injured 300 people.
"Immediately after the bombing, which I am guilty of, if there's any lingering doubt about that, let there be no more," he said. "I did do it along with my brother."
On June 25, Tsarnaev was transferred to a maximum-security prison in Colorado.