A new method is proposed to deal with the rotationally inelastic scattering of A+BC collision system. The matrix element 0,l/?)t|R′> is obtained analytically, the centrifugal potential takes the CS approximation, the rotationally term in the total Hamiltonian is treated by the Fourier transform and the time-dependent Schrodinger equation is approximated by the SOD method. Using this method the opacity function for Ar+N2 scattering system is calculated. The results show that the method introduced in the present paper is more suitable than the CCWP method in calculating the transition for long-range Ar+N2 potentials. And the calculational efficiency of our method is higher than the latter.