Focusing on the problem of solving coupled Logistic fractional-order differential equation, a discretization method was introduced to solve it discretly. Firstly, a coupled Logistic integer-order differential equation was introduced into the fields of fractional-order calculus. Secondly, the corresponding coupled Logistic fractional-order differential equation with piecewise constant arguments was analyzed and the proposed discretization method was applied to solve the model numerically. Then, according to the fixed point theory, the stability of the fixed point of the synthetic dynamic system was discussed, and the boundary equation of the first bifurcation of the coupled Logistic fractional-order system in the parameter space was given. Finally, the model was numerically simulated by Matlab, and more complex dynamics phenomena of model were discussed with Lyapunov index, phase diagram, time series diagram and bifurcation diagram. The simulation results show that, the proposed method is successful in discretizing coupled Logistic fractional-order differential equation.