Hydrogen is expected as new fuel instead of fossil fuel. It will be used as fuel of a fuel cell for which development is performed actively. But it is difficult to experiment the hydrogen dispersion in case of hydrogen leaks. Therefore clarifying the hydrogen dispersion with numerical analysis becomes important. Furthermore, hydrogen dispersion under various conditions can be clarified with numerical analysis, which is useful to use hydrogen safely. This paper deals with computer simulation of the hydrogen dispersion by a finite element method. The mathematical model of hydrogen dispersion is governed by the momentum equations, the continuity equation and the hydrogen mass conservation equation. The model presented here is a three-dimensional, incompressible, non-stationary model. This paper describes a finite element method with the stabilization technique for solving Navier-Stokes equations and the advection diffusion equation for hydrogen concentration like the Boussinesq approximation of thermal convection problems. Improved numerical results are also shown.