To address the problem that the solution accuracy of the sparrow search algorithm (SSA) depends on the population at the better location and is easily trapped in the local optimum, this study proposes an improved sparrow search algorithm (ISSA). The algorithm firstly proposes a normal shift strategy to shift the population with the center of gravity as the guide to achieve the decay of the normal distribution of the moving energy and effectively improve the exploration ability of the population for local search. Secondly, it introduces a dynamic sinusoidal perturbation strategy to achieve the two-way demands of the discoverer for the early search step and the late fast convergence through the scaling factor. Then, a backward learning mechanism is added for the poorly positioned early warners in the sparrow population to generate the backward solution of the perturbation with their current position, which is helpful to expand the search step and enable the algorithm to jump out of the local optimum. Finally, six test functions are randomly selected and compared with other similar algorithms, and the experimental results verify the effectiveness of the ISSA algorithm.