Statistical researchers have shown increasing interest in generating truncated multivariate normal distributions. In this paper, we only assume that the acceptance region is convex and we focus on rejection sampling. We propose a new algorithm that outperforms crude rejection method for the simulation of truncated multivariate Gaussian random variables. The proposed 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 over the proposal probability density function. The simulation results show that the method is especially efficient when the probability of the multivariate normal distribution of being inside the acceptance region is low.