In this study, we introduce a matrix variate skew Laplace distribution as a variance-mean mix-ture of the matrix variate normal and the scale inverse gamma distribution. The proposed distribution is a generalization of the multivariate skew Laplace distribution studied by [1]. We explore some distributional properties of the proposed distribution such as the probability density function and the characteristic function. Also, we study the estimation of the parame-ters and give an EM algorithm to obtain the estimates of the parameters. Then, we give a small simulation study to illustrate the performance of the proposed EM algorithm for finding the estimates.