A generalized gyrokinetic Poisson solver has been developed and implemented in gyrokinetic particle simulation of low frequency microinstabilities in magnetic fusion plasmas. This technique employs local operations in the configuration space to compute the polarization density response and automatically takes into account the background profile effects contained in the gyrokinetic Poisson equation. It is useful for the global gyrokinetic simulation of magnetized plasmas in general equilibria, where the traditional spectral method is not applicable. The numerical scheme is also most amenable to massively parallel algorithms.