In this paper we propose a new blind adaptive compensator associated with the inverse QRD-RLS (IQRD-RLS) algorithm to adaptively estimate the parameters, related to the effects of gain/phase imbalance and DC offsets occur in the Quadrature demodulator, for compensation. In this new approach the power measurement of the received signal is employed to develop the blind adaptation algorithm for compensator, it does not require any reference signal transmitted from the transmitter and possess the fast convergence rate and better numerical stability. To verify the great improvement, in terms of reducing the effects of the imbalance and offset, over existing techniques computer simulation is carried out for the coherent 16 PSK-communication system. We show that the proposed blind scheme has rapidly convergence rate and the smaller mean square error in steady state.