The unified coupled-mode theory for long-period-grating-coupler is obtained by deriving directly from Maxwell’s equation when all the modulation effects of refractive-index, gain and loss are considered. Then, the characteristics of power coupling and signal filtering between the straight-arm and cross-arm of complex-modulated long-period-grating-coupler are investigated thoroughly. The results demonstrate that monodirectional nonreciprocal power coupling is shown when gain/loss is equal with refractive-index modulation. In addition, the complex-modulated long-period-grating-coupler shows different add/drop filtering characteristics if the multiplexed signals are injected from different fibers or directions. For the gain modulation, the phase-matched signal is coupled into the cross-arm and is amplified simultaneously. But for the loss modulation, the signals in straight-arm and cross-arm remain their respective original input power, and can not be filtered according to their wavelengths any more.