The free-item extrapolated multistep method for precise integration is proposedfor a nonlinear system, and the calculation formula for the free-item extrapolated multistep method is obtained. The accuracy of the extrapolated multistep me thod can be improved through increasing the number of extrapolated points; at th e same time, evaluations cannot be increased too much. The precise integration m ethod has been developed and perfected by the present studies. When the method i s applied to a chaotic system, the result is admirable. Numerical calculations s how that the present method is high by accurate and computationally efficient.It has more advantages than the traditional methods in the analysis of a chaotic s ystem.