He filed an appeal with the Supreme Judicial Court.
His attorney is expected to argue police illegally seized evidence from his home.
The defense also says the trial judge didn’t allow sufficient questioning to find out if the jurors had any bias.
Entwistle is serving a life sentence.
Prosecutors alleged he killed his family because he’d become despondent over his business failings and debt.
Entwistle said he came home from running errands to found his wife and 9 month old child dead.