The Burg algorithm is suitable for inter-harmonic estimation， but， in the presence of noise， the estimated spectral results will be biased or even erroneous. A new Burg adaptive algorithm based on the higher-order cumulant is put forward to estimate the inter-harmonic signals. First， this paper introduces the principle of Burg algorithm， and modifies the error prediction power of the algorithm based on the fact that higher-order cumulant is insensitive to Gaussian noise. Then， the recursive form is presented to calculate the reflectance so as to reduce the calculation workload brought about by the cumulant. Finally， the fourth-order cumulant diagonal slice of the inter-harmonic signal is proposed to estimate the amplitudes of various components. Simulation results show that the method proposed can markedly improve the spectral estimation performance while yielding accurate inter-harmonic frequency and amplitude even in a noisy environment.