We apply the Hermite integrate to nonlinear stochastic finite element method, and establish the theory and algorithm of Stochastic FEM based on the Hermite integrate. An example is put forward, which is solved by choosing different kinds of integrate points and verified with Monte-Carlo stochastic FEM. The result show that the new method own a high efficiency. On the precision, the first and the second order quadrature reach high precision although the integrate points only is 3, however, the high precision of the third and the fourth order quadrature need more integrate points (e.g.11).