Wave-breaking free pulses generated in passively mode-locked fiber lasers can tolerate a certain cubic phase delay induced by third-order dispersion without losing pulse quality. We demonstrate that the spectral as well as the temporal profile of the pulses become asymmetric. The generated pulses had a pulse energy up to 3.5nJ and could be externally compressed down to 145fs . The fact that the pulses could always be dechirped within 10\% of the Fourier limit points out the linearity of the chirp. The pulse asymmetry was also observed in the output coupling characteristic of the mode-locking mechanism.