Abstract: If the disturbing gravity gradients are expressed by earth-centered spherical coordinates in the local north-oriented reference frame, the first- and second-order derivatives of the Legendre functions of the colatitude and the sine function of colatitude in the denominator which tend to infinity when the computational point is approaching the poles. Therefore, the non-singular computational formulas of the first- and second-order derivatives of the Legendre functions of the colatitude and the are introduced, and the non-singular computational formula of is also deduced. When taking the non-singular computational formulas of the first- and second-order derivatives of the Legendre functions of the colatitude and the 、 into the computation of each component of the disturbing gravity gradients, the complex situation that the m equals to 0, 1, 2, and any other numerical values are also considered, and the non-singular particular computational models of each component of the disturbing gravity gradients are constructed. The simulation experimentation shows that the particular computational models constructed in this paper not only completely fulfill the precision demand of the computation of the current satellite gravity gradients, and the models are steady, credible and easy to be programmable realized.