Recent communications standards, such as vehicle-to-vehicle and fifth generation, include applications where the transmitted signal encounters rapid changes of propagation scenarios, resulting in wireless links characterized as non-stationary (NS) channels. Hence, channel models that correctly explain and represent the measured time-varying channel statistics, and their associated simulation methods for testing purposes, are all required. Although the body of works devoted to NS channel modeling is vast, due to the complexity and variety of this problem, the provided NS statistics are defined only within a limited observation time, and therefore, the generated channel realizations do not include the changes between scenarios. In light of this problem, this paper introduces a channel model that mimics the continuous change of the mobile propagation channel via a continual renewal of channel parameters, in which all stationary and NS channels are represented under a unified structure. Theoretical and simulation results provided in this paper confirm that the proposed model reproduces stationary models with high accuracy. In addition, NS channel realizations with predefined time-varying power spectral density and time-varying envelope distributions are also shown in this paper, providing a means for testing modern communications systems.