Based on the Weizs?cker formula, five coefficients of nuclear binding energy were recalculated by the covariance analysis method to minimize the average error of the nuclear binding energy. The covariance method given by Fattoyev was used to give out the error ranges of each coefficient, the correlation coefficient between each coefficient and the nuclear binding energy, and the coefficient of correlation between coefficients themselves. The research shows that the nuclear binding energy is closely related with the symmetry energy, surface energy and Coulomb energy. The error of the symmetry energy coefficient is large, which suggests that three important physical laws are involved here:the nucleus may have quadrupole deformation; the size of Coulomb energy may change because of the quadrupole deformation; there may exist neutron skins and proton skins that affect the size of the symmetry energy. By the study, the correlation between the coefficients can be compared, the number of coefficients can be reduced and the information of the binding energy and the close relationship between the volume term and surface item can be got. The results provide a theoretical basis for achieving a more accurate value of nuclear mass.