In this paper, we will investigate a multigrid algorithm for poroelasticity problem by a new finite element method with homogeneous boundary conditions in two dimensional space. We choose N\'ed\'elec edge element for the displacement variable and piecewise continuous polynomials for the pressure variable in the model problem. In constructing multigrid algorithm, a distributive Gauss-Seidel iteration method is applied. Numerical experiments shows that the finite element method achieves optimal convergence order and the multigrid algorithm is almost uniformly convergent to mesh size $h$ and parameter $\delta t$ on regular meshes.
Poroelasticity problem, finite element method, multigrid method.