In the bounce inflation scenario, the inflation is singularity-free, while the advantages of inflation are preserved. We analytically calculate the power spectrum of its primordial gravitational waves (GWs), and show a universal result including the physics of the bounce phase. The spectrum acquires a cutoff at large scale, while the oscillation around the cutoff scale is quite drastic, which is determined by the details of bounce. Our work highlights that the primordial GWs at large scale may encode the physics of the bounce ever happened at about ∼60 efolds before inflation.