Using the fast Fourier transform (FFT) algorithm to make the solution of paraxial wave equations, we develop a x ray laser wave optics code XWAVE based on a model of amplified spontaneous emission(ASE). It includes diffraction, gain saturation, and refractive effects due to electron density gradients. The results of coherence, spatial distribution and angular distributions of x ray laser are presented, which agrees with the results of gain coefficients and angles of divergence in the multi-target experiments.