A memristor is a non-linear element. The chaotic system constructed by it can improve its unpredictability and complexity. Parameter identification of a memristive chaotic system is the primary task to implement chaos control and synchronization. To identify the unknown parameters accurately and quickly, we introduce the Sine Pareto Sparrow Search Algorithm (SPSSA), a modified sparrow search algorithm (SSA). in this research. Firstly, we introduce the Pareto distribution to alter the scroungers’ location in the SSA. Secondly, we use a sine-cosine strategy to improve the producers’ position update. These measures can effectively accelerate the convergence speed and avoid local optimization. Thirdly, the SPSSA is used to identify the parameters of a memristive chaotic system. The proposed SPSSA exceeds the classic SSA, particle swarm optimization algorithm (PSO), and artificial bee colony algorithm (ABC) in simulations based on the five benchmark functions. The simulation results of parameter identification of a memristive chaotic system show that the method is feasible, and the algorithm has a fast convergence speed and high estimation accuracy.