The finite element method is used to obtain numerical solutions of the Schrödinger equation for the Helium 1s2p-state. The relative errors of approximate energies are 10^-6 for triplet and 10^-4 for singlet which are slightly smaller than J. Shertzer's results for the Helium ground state[9]. The generalized eigenvalue problems obtained by FEM are symmetric for the ground state but unsymmetric for 1s2p-state. It becomes more difficult to solve the problems. Form the graphs of wave functions, it can be seen that it is reasonable to solve the Schrödinger equations in bounded domains.