The affine-projection-like (APL) algorithm is reported to achieve lower computations than affine-projection algorithm (APA) without compromising the steady-state performance. Further, the performance accuracy of the adaptive feedback canceller (AFC) in hearing aids is enhanced using an improved proportionate APL (IPAPL) algorithm. Two new learning algorithms are proposed for AFC, which apply the memory of previous gain factors and μ-law proportionate technique to the IPAPL, termed as memorised IPAPL (MIPAPL) and μ-law MIPAPL (MMIPAPL), respectively. In addition, a segmented approach is also suggested which offers computational advantage over MMIPAPL. The results obtained from simulation-based experiments demonstrate that the proposed methods achieve faster convergence rate than the existing methods.