This paper presents an empirical study on the influence of approximation approaches on accelerating the fireworks algorithm search by elite strategy. In this study, we use three sampling data methods to approximate fitness landscape, i.e. the best fitness sampling method, the sampling distance near the best fitness individual sampling method and the random sampling method. For each approximation methods, we conduct a series of combinative evaluations with the different sampling method and sampling number for accelerating fireworks algorithm. The experimental evaluations on benchmark functions show that this elite strategy can enhance the fireworks algorithm search capability effectively. We also analyze and discuss the related issues on the influence of approximation model, sampling method, and sampling number on the fireworks algorithm acceleration performance.