The finite element method in electromagnetics has been puzzled by spurious solutions because electric field divergence is not imposed zero condition. In the paper Maxwell equations are given in frequency domain for the electromagnetic resonant cavity. By further introducing Lorentz condition, The 2 types variational principles with 2 kinds and 3 kinds of variables are conducted respectively. Based on that, a new method of node finite element for electromagnetic resonant cavity is proposed for avoiding spurious solutions, and the cavity eigenvalues are got with subspace iteration method. Numerical results illustrate the feasibility and effectiveness of this method in the paper.