In this paper we consider the parameter estimation of the multivariate skew-slash distribution introduced by Arslan [Arslan, O. 2008. An alternative multivariate skew-slash distribution. Statistics and Probability Letters 78, 2756-2761], which is a recent example of the normal variance-mean mixture distributions. Due to the complexity of the likelihood function, estimation of its parameters by direct maximization of the likelihood function seems difficult. To overcome this problem, we propose a simple EM-based maximum likelihood estimation procedure to estimate the parameters of the multivariate skew-slash distribution. We provide three examples to demonstrate the modeling strength of the multivariate skew-slash distribution and the feasibility of the proposed EM algorithm. (C) 2009 Elsevier B.V. All rights reserved.