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The leaky integrator echo state network (Leaky-ESN), an improved echo state network (ESN), has been proved to be useful for learning very low dynamic systems. However, the Leaky-ESN exists a complex nonlinear relationship between parameters, and then setting parameter values is very difficult because of lacking effective guiding principles. It is difficult for beginners to give suitable values of the parameters. Therefore, in order to further enhance modeling ability, in this paper, we study the relationship between the size, sparsity of the reservoir and the modeling accuracy through the simulation experiment. This paper not only gives the qualitative description of relationship between them, but also gives the quantitative description by the least squares fitting method. It is worth mentioning that this paper gives an effective principle about how to choose the size and the sparsity of the reservoir.