Statistical researchers have shown increased interest in generating of truncated multivariate normal distributions. In this paper, we assume that the acceptance region is convex and our focus is on the rejection sampling. We propose a new algorithm that outperforms crude rejection method for the simulation of truncated multivariate normal distribution. Our algorithm is based on a generalization of Von Neumann’s rejection technique which requires the determination of the mode of the truncated multivariate density function. We provide a theoretical upper bound for the ratio of the target probability density function that the proposed density function is defined from the mode. This algorithm is used in the case where the maximum likelihood lies outside the acceptance region and the dimension of the multivariate density is high. The simulation results show that using rejection sampling from the mode is more efficient than the usual rejection sampling. In order to support the theoretical aspect of our work, we have used an illustrative example.