In this paper,we analyse the rate of convergence of some precontditionedonjugate gradient methods,namely ICCG method ILUCG(k) method, ILUCG (p)method and so called "TCG method" with a number of splittings for preconditioning the coefficient matrix A of the system of linear algebraic equation to be solved under the condition that A is diagonally dominant. Several numeriical examples are given to illustrate our analysis.