Photoacoustic tomography seeks to reconstruct an acoustic initial pressure distribution from the measurement of the ultrasound waveforms. Conventional methods assume a-prior knowledge of the sound speed distribution, which practically is unknown. One way to circumvent the issue is to simultaneously reconstruct both the acoustic initial pressure and speed. In this article, we develop a novel data-driven method that integrates an advanced deep neural network through model-based iteration. The image of the initial pressure is significantly improved in our numerical simulation.