A new simulation algorithm of random phase screen time series for the purpose of generating dynamically atmospheric turbulence distorted wave fronts using Zernike polynomials is described in this paper. Both spatial and the temporal statistics of atmospheric turbulence are considered in this technique. Turbulence phase is simulated by using a set of random-process-generated Zernike coefficients. Not only Kolmogorov but also non-Kolmogorov statistical spectrum can be modeled successfully using this algorithm. Our results show that smooth time-evolving turbulence wave fronts can be generated perfectly at given time frequency interval.