We theoretically propose a scheme to achieve all-optical nonreciprocal magnon lasing action in a composite cavity optomagnonical system considering of a yttrium iron garnet sphere coupled to a parametric resonator. The magnon lasing behavior can be engendered via the magnon-induced Brillouin scattering process in the cavity optomagnonical system. By unidirectionally driving the χ(2)-nonlinear resonator with a classical coherent field, the squeezed effect occurs only in the selected direction due to the phase-matching condition, resulting in asymmetric detuning between the two resonators, which is the physical mechanism to generate a nonreciprocal magnon laser. We further examine the gain factor and power threshold of the magnon laser. Moreover, the isolation rate can reach 21 dB by adjusting the amplitude of the parametric amplification. Our work shows a path to obtain an all-optical nonreciprocal magnon laser, which provides a means for the preparation of a coherent magnon laser and laser protection.