The key issue in accelerating method of char-acteristics (MOC) transport calculations is in obtaining a completely equivalent low-order neutron transport or dif-fusion equation. Herein, an equivalent low-order angular flux nonlinear finite difference equation is proposed for MOC transport calculations. This method comprises three essential features: (1) the even parity discrete ordinates method is used to build a low-order angular flux nonlinear finite difference equation, and different boundary condition treatments are proposed; (2) two new defined factors, i.e., the even parity discontinuity factor and odd parity dis-continuity factor, are strictly defined to achieve equiva-lence between the low-order angular flux nonlinear finite difference method and MOC transport calculation; (3) the energy group and angle are decoupled to construct a symmetric linear system that is much easier to solve. The equivalence of this low-order angular flux nonlinear finite difference equation is analyzed for two-dimensional (2D) pin, 2D assembly, and 2D C5G7 benchmark problems. Numerical results demonstrate that a low-order angular flux nonlinear finite difference equation that is completely equivalent to the pin-resolved transport equation is established.