Abstract: The signal reconstruction algorithm is the key to compressed sensing. Signal reconstruction based on approximate l\-0 norm chooses a continuous function to estimate l\-0 norm, thus the minimization problem of l\-0 norm is transformed into an optimization problem of a smooth function. It is critical for the signal reconstruction algorithm to select the appropriate smooth function and optimization algorithm. To improve the accuracy of the sparse signal recovered in the compression sense, the sum of a simple fractional function is proposed to approximate l\-0 norm on the basis of previous work in the paper. Then the sparse solution of an unconstrained optimization problem of the function is solved by Newton iterative algorithm, which effectively integrated the advantages of the fast convergence of approximate l\-0 norm algorithm and the high precision of Newton iteration algorithm. Thus, the minimization of l\-0 norm is approximated smoothly and efficiently within less time. The performance of the proposed algorithm is tested and compared with some existing similar algorithms in the case of different compression ratio, sparseness and noise levels in the simulation experiments. Simulation results show that the performance of the proposed algorithm is better than the existing similar algorithms, and the precision of reconstructed signal is greatly improved, which improves the signal recovery quality in compressed sensing effectively under the same conditions.