This work is devoted to the numerical resolution of the 4D Vlasov equation using an adaptive mesh of phase space. We previously proposed a parallel algorithm designed for distributed memory architectures. The underlying numerical scheme makes possible a parallelization using a block-based mesh partitioning. Efficiency of this algorithm relies on maintaining a good load balance during the whole simulation. In this paper, we propose a dynamic load balancing mechanism based on a relevant cost metric and a geometric partitioning algorithm. This mechanism is deeply integrated into the parallel algorithm in order to minimize overhead. Performance measurements on a PC cluster show the good quality of our load balancing and confirm the pertinence of our approach.