  We develop an event generator, NLL-QEDPS, based on the QED shower including
the next-to-leading logarithm correction in the e^+e^- annihilation. The shower
model is the Monte Carlo technique to solve the renormalization group equation
so that they can calculate contributions of alpha^m log^n(S/m_e^2) for any m
and n systematically. Here alpha is the QED coupling, m_e is the mass of
electron and S is the square of the total energy in the e^+e^- system. While
the previous QEDPS is limited to the leading logarithm approximation which
includes only contributions of (alpha log(S/m_e^2))^n, the model developed here
contains terms of alpha(alpha log(S/m_e^2))^n, the the next-to-leading
logarithm correction.
  The shower model is formulated for the initial radiation in the e^+e^-
annihilation. The generator based on it gives us events with q^2, which is a
virtual mass squared of the virtual photon and/or Z-boson, in accuracy of
0.04%, except for small q^2/S.
