AbstractThis work deals with the kinetics of the living polymerization initiated by a bifunctional initiator with different rate constants of the first and the second step of initiation. The expressions of the molecular weight distribution (MWD) function, the number‐ and weight‐average degrees of polymerization and the polydispersity index were derived rigorously. Numerical results show that the nonequal initiation rate constants often lead to a bimodal MWD except the ratio ofkitoki′ being very large (>500, for instance) or relatively small (<1, for example). The MWD of the resultant polymer is rather narrow even in the presence of double peaks. With decreasing initiator concentration, the MWD at full conversion becomes narrower, and the shoulder peak of the MWD curve dec