The theoretical formulae for the influence of the change of the theoretical formulae for the influence of the change of moment of inertia due to a time variation of the gravitational constant on the period of a pulsar are given by the method for solving the first order linear differential equations. The analytical and numerical solutions of the period of a pulsar slow down due to time variation of the gravitational constant are derived and calculated for five pulsars (PSR1749-28, PSR2045-16. JP1933+16, P1508+55 and CP0834+06). Numerical results are given in Table.1 The results are discussed and conclusions are given.