A parabolic pulse generator based on non-reciprocal nonlinear optical fiber loop mirror is proposed. When an incident triangular optical pulse is split into two branches of the loop mirror, two coherent light fields with linear intensity profile are counter-propagated in the interferometer and suffer different nonlinear phase shift caused by self-phase modulation. Because the intensity of interference field is determined by the amplitudes and phase relationship between two coherent lights, the interference result gives parabolic pulse. This concept is verified by theoretical analysis and simulation. In the experiment, tunable bright and dark parabolic pulses with repetition frequencies of 8, 9, and 10 GHz are simultaneously generated, which agree with the theoretical expectation well and exhibit large operation bandwidth.