A new fast and accurate scheme is introduced to simulate the Raman backscattering of laser pulses in a plasma. In the proposed method, the envelope-kinetic equation of a plasma wave is solved along with conventional laser envelope equations. The kinetic term, which is the most noticeable feature of the envelope-kinetic plasma equation, can be self-consistently solved by employing some test particles. The benchmarkings of the new code against the averaged particle-in-cell results show quite a reasonable agreement, while the computation speed is enhanced by more than a factor of ten.