In order to make a theoretical description of the multi-wavelength active coherent beam combination(CBC), and to figure out the significant factors influencing the combination effect, a mathematical model was established based upon the fundamentals of CBC. The combination effect of each frequency component and the whole combination effect are obtained on the calculation of the nine-wavelength seven-channel CBC example with various optical path differences. Only the central frequency component is coherently enhanced and the whole combination effect degenerates to non-coherent beam combination on the condition of large optical path difference. More components are coherently enhanced and the whole combination effect is improved when the optical path difference is small. The optical path difference is the key in multi-wavelength active CBC. To achieve excellent combination effect, the optical path difference should be adjusted to the same and then the phase of each channel is locked.