Abstract: When both the input and the output of a IIR system are corrupted by α-stable noises， the classical least mean lp-norm (IIR_LMP) algorithms usually provide a large biased solution. A total least mean lp-norm (TLMP) algorithm for adaptive IIR filtering is discussed in this paper in which α-stable noise interferences of the input and the output are total considered and random gradient method is used in the least lp-norm Rayleigh quotient to obtain the adaptive IIR filtering equation. The simulation is performed to evaluate the influence of the main parameters such as character index and step factor on the performance of the TLMP algorithm. In time-varying system and time-invariant system， the performances of the TLMP algorithm and the LMP algorithm are compared and the results indicate that TLMP algorithm has faster convergence speed and less error.