In an effort to understand early-stage polymer crystallization and the recently proposed spinodal mode of crystallization, we have performed Brownian dynamics simulations of crystallizing polymer chains. We find that the mechanism of polymer crystallization is nucleation and growth even in the induction period, although scattering data can he superficially fitted to the spinodal decomposition description. The microscopic model used in our simulations reveals rich details of the kinetic pathway of polymer crystallization in very early stages.