Abstract: The adaptive beamforming algorithm based on Interference plus Noise Covariance Matrix （INCM） reconstruction cannot accurately calculate the power of non-uniform noise. This paper proposes an adaptive beamforming algorithm based on Maximum Inter-element Spacing Constraint （MISC） array to address this problem. Firstly， the noise-free covariance matrix and the non-uniform noise covariance matrix are estimated using matrix completion technique. Then the noise-free covariance matrix is ​​used to estimate the Direction of Arrival （DOA） and power of the incident signal. Finally， INCM is reconstructed. With the accurate estimation of the non-uniform noise power by the matrix completion technique and the high degree of freedoms provided by the MISC virtual difference co-array， the proposed algorithm can reconstruct INCM more accurately under non-uniform noise. Simulation results demonstrate the effectiveness of the proposed algorithm.