We report pulse trapping in passively mode-locked fiber lasers operating in a near-zero dispersion regime. Two polarization components of vector pulses have different central wavelengths while copropagating as a unit in fiber lasers. The vector pulses exhibit smooth Gaussian spectral profile without any sidebands, qualitatively distinct from those observed in net-anomalous and net-normal fiber lasers. Numerical simulations suggest that the pulse trapping depends not only on fiber birefringence and cavity dispersion but also on saturable absorption effect. The experimental observations are in good agreement with the numerical simulations.