We present a parallel algorithm for solving the 4D Vlasov equation. Our algorithm is designed for distributed memory architectures. It uses an adaptive numerical method which reduces computational cost. This adaptive method is a semi-Lagrangian scheme based on hierarchical finite elements. It involves a local interpolation operator. Our algorithm handles both irregular data dependencies and the big amount of data by distributing data into blocks. Performance measurements on a PC cluster's confirm the pertinence of our approach. This work is a part of the CALVI project.