When the computational point is approaching the poles, the variance and covariance formulae of the disturbing gravity gradient tensors tend to he infinite, and this is a singular problem. In order to solve the problem, the authors deduced the practical non-singular computational formulae of the first-and second-order derivatives of the Legendre functions and two kinds of spherical harmonic functions, and then constructed the nonsingular formulae of variance and covariance function of disturbing gravity gradient tensors.