Abstract: Deep neural network(DNN) is shown converges faster in low frequencies. Taking advantage of this fact, we propose a phase shift deep neural network (PhaseDNN) for a frequency uniform convergence in approximating high frequency functions and solutions of wave equations. PhaseDNN constructs a series of moderately-sized DNNs for selected high frequency ranges. With the help of phase shifts in the frequency domain, each of the trained DNNs can approximate a function’s specific high frequency range at the speed of low frequency learning.  The PhaseDNN is then applied to learn the solution of high frequency wave problems in inhomogeneous media through the least square residuals of either differential or integral equations.