Designing the trans-lunar orbit is one of the key skills for lunar probe mission, and the differential correction is proved to be one of the effective methods to solve a non-linear iteration equation. According to the requirements of high design precision and rapid calculation speed in designing the trans-lunar orbit, a rapid trans-lunar orbit design method from improved differential correction was proposed. Based on the dynamical model, which contains the sun, the earth, the moon, and the earth's J₂ perturbation force in the DE405/LE405 planet and lunar-ephemeris data, the partial derivative matrix of parameters from the perilune to the perigee was deduced. The differential correction matrix was integrated in company with the orbital state variables and velocity, and the transfer orbit design parameters were converged iteratively and rapidly with the precise differential correction matrix. Simulation result shows that the convergence rate of the integral differential correction method is faster than the frequently-used SQP（Sequential Quadratic Programming）method in dynamical models with the same accuracy.