Free-space optical (FSO) communication may be severely influenced by the inevitable turbulence effect that results in channel gain fluctuations and fading. The objective of this paper is to provide a simple and effective simulator of the weak-turbulence FSO channel that emulates the influence of the temporal covariance effect. Specifically, the proposed model is based on lognormal distributed samples with a corresponding correlation time. The simulator is based on the solution of the first-order stochastic differential equation (SDE). The results of the provided SDE analysis reveal its efficacy for turbulent channel modeling.