This paper describes a parallel implementation of a numerical solver for the Vlasov equation. The solver is based on a kinetic model describing the motion of charged particles in a plasma. The evolution of the distribution of particles in phase space is computed with an explicit method, and we take into account the self-consistent electric field through the coupling with a Poisson type equation. In this paper, we focus on a recently developed 5D parallel numerical application dedicated to gyrokinetic simulation of tokamak systems and ITG turbulence simulation. A semi-Lagrangian Vlasov solver is used. A specific cubic spline interpolation allows us to formulate a domain decomposition method. A hybrid MPI/OpenMP paradigm was used to benefit from a large number of processors while reducing communication costs.