We present a passively mode-locked erbium-doped fiber ring laser with near-zero net cavity dispersion using the nonlinear polarization rotation technique. The compact all-fiber laser is constructed by utilizing an optical integrated component. Through optimizing the cavity dispersion and nonlinearity, high-peak-power near-transform-limited pulses with a spectral width beyond the gain bandwidth limitation can be directly obtained from the laser. Resultant output pulses have a pulse duration of 62 fs, a 3-dB spectral width of 66.3 nm, and a maximum peak power of 7.9 kW. Numerical simulations reproduce the generation of sub-100-fs pulses in the laser. The pulse-shaping mechanism can be attributed to simultaneous dispersion and nonlinearity management in the cavity, which is distinct from that in the stretched-pulse lasers.