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For the channel estimation problem under α-stable distributed impulse interference, the traditional fixed-step adaptive filtering cannot satisfy the fast convergence speed and low steady-state error at the same time, whereas the variable-step method is able to effectively solve this contradiction. This paper proposes an improved variable step-size least mean p-power adaptive algorithm that offers good robustness against impulsive noise. The proposed algorithm takes into account the linkage between the errors and uses the adjustment of the step size based on the errors of the current moment and the previous k moments, thus overcoming the problems of poor anti-noise performance and large steady-state fluctuations of the fixed-step size algorithm. This algorithm ensures that the step size does not change abruptly when the system is disturbed by impulse noise and can achieve a lower steady-state error. The simulation results show that the algorithm has better convergence than the traditional fixed step-size algorithm and the existing variable step-size algorithm under the interference of impulsive noise. [ABSTRACT FROM AUTHOR]