For the anionic polymerization of polar monomer initiated by arbitrarily function-al initiator with instantaneous initiation and monomer termination，the expressions of molecular weight distribution，average degree of polymerization，functionality distribu-tion and average functionality of the polymer formed have been derived by means of non．steady state method．The maximum amount of the monomer which will be con-sumed during the polymerization under consideration was discussed．A theoretical method has been established．with which the molecular weight distribution and the values of other molecular parameters can be calculated from the monomer conversion and initial conditions of the polymerization．It was shown that with a few exceptions．the theore-tical curves of molecular weight distribution resulted from numeric computation possess double peaks．Such a process is particularly true for the anionic polymerization of methyl methacrylate in polar solvents and at lower temperature．