A recursive total least l_p-norm (RTLMP) algorithm is developed to recursively compute the total least l_p-norm solution for adaptive finite impulse response(FIR) filters.Due to the existence of the non-Gaussian α-stable noise,the performance of signal processing algorithms designed under the Gaussian assumption may degrade seriously.In this paper,a new adaptive algorithm based on the classical power iteration is developed which can minimize the L_p norm of the error function.The performance of the algorithm is evaluated via simulations.It is shown that the new algorithm achieves superior convergence rate.