This paper presents an adaptive feedback canceller (AFC) based on a pseudo affine projection (PAP) algorithm that can provide fast and stable adaptation to the time-varying environment. The proposed algorithm utilizes the adaptive linear prediction (LP) to obtain the LP coefficients of input signal model and the inverse gain filter (IGF) to alleviate the effect of compensation gain. As a result, when the input is model as an AR signal, the proposed algorithm satisfies the condition for having an almost unbiased estimatie of the feedback path and then its performance is relatively independent of the gain setting of hearing aids. Simulation results showed that the proposed algorithm is capable of obtaining unbaised feedback path estimates and high speech quality.