Abstract: In view of the Delay-Doppler (DD) domain sparse structure, estimation of doubly-spread UWA channel can be converted to the problem of sparse recovery under the framework of compressed sensing to achieve performance gain. Although the classic sparse recovery methods such as 11 norm, or approximated l₀ norm algorithms are subject to performance degradation at the presence of various sparsity pattern of the UWA channels, greedy methods including MP (matching pursuit) and OMP (orthogonal matching pursuit) suffer from the drawbacks of local minima traps. A newly defined non-uniform norm constraint (NNC) is proposed to assign into the two dimension objective function of the DD domain sparse recovery, i.e., sparse components in the DD domain are uniformly formulated as 11 norm or l₀ norm constraint according to relative magnitude, to enable sparsity adaptability at the form of different 11 norm or 10 norm mixture. Meanwhile, the iterative method for NN domain sparse recovery is derived by the gradient descent recursion and projecting the solution of which to feasible set. Numerical simulation validates the performance improvement of the proposed algorithm compared to the traditional methods. Furthermore, the UWA communication experimental results demonstrate the superiority of the proposed method in the form of an equalizer driven by channel estimator.