We investigate the effects of a piece of zero-dispersion fiber (ZDF) on the pulse dynamics of a passively mode-locked fiber laser operating in the stretched-pulse regime. Numerical simulation suggests that the proper location and length of ZDF facilitate spectrum broadening and pulse shortening in fiber lasers while maintaining constant net cavity dispersion. A nonlinear polarization evolution mode-locked Er-doped fiber laser with a dispersion map is built based on the simulation. Larger optical spectrum broadening is obtained by inserting a longer ZDF after the active fiber during single-pulse operation, which well agrees with the simulation.