We present a new method to calculate Raman intensity from density functional calculations: the RASCBEC. This method uses the Born effective charge (BEC) instead of the macroscopic dielectric tensor used in the conventional method. This approach reduces the computational time tremendously for molecular crystals or large amorphous systems, decreasing the computational process cost by a factor of $N/8$, where $N$ is the total number of atoms in the simulation unit cell. When $N$ is larger than $8$, our method shows advantage over conventional methods. A first test of the new method on the crystal GeO$_2$ yields results in good agreement with both the conventional theoretical method and experimental data. The effect of varying electric field strength used to compute numerically the derivative of the Born effective charge by electric field, is also tested and summarized. We then apply RASCBEC to a large magnetic molecular crystal that has 448 atoms in a unit cell and to an amorphous Ta$_2$O$_5$ sample that has 350 atoms. Consistency among the results calculated with our method, the conventional method, and experimental data remains. Timing information of the two methods is provided, and we clearly see that RASCBEC saves tremendous computation time.