This work dealt with the kinetics of Living polymerization initiated by a trifunctional initiator with nonequal initiation rate constants by way of the Laplace transformation and graphical method. The expressions of the molecular weight distribution function, the number-and the weight-average degrees of polymerization, and the distribution of branching were derived rigorously. The numerical results show that the influence of nonequal initiation rate constants on the molecular parameters of the resulting polymer is important at low monomer conversion and becomes negligible at high polymer yield.