Aiming at the problems of low estimation accuracy and slow convergence of existing array signal direction of arrival(DOA)estimation algorithms, a DOA estimation algorithm based on hyperbolic composite function approximating the l0 norm is proposed. Firstly, a hyperbolic composite function is given to approximate the l0 parametric number, and the problem of solving the l0 parametric minimum is transformed into the optimization problem of solving the hyperbolic composite function. Then, to improve the global convergence efficiency of the algorithm, the modified Newton method is used to optimally solve the hyperbolic composite function. The approximate l0 norm solution is obtained through the inner and outer loops of the algorithm. The outer loop provides the approximation factor for the inner loop, and the inner loop solves the modified Newton iterative expression according to the decreasing approximation factor. Finally, the optimal solution of the hyperbolic compound function is obtained, from which the DOA estimate is obtained. The effectiveness of the proposed algorithm is verified by simulation experiments, The results show that the root mean square error of DOA estimation is 0.685 6° for the proposed algorithm with a signal-to-noise ratio of 5 dB, and the estimation success rate is higher than 98%.