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In this paper, based on the basic principle of the SPH method's kernel approximation, a new kernel approximation was constructed to compute rst order derivative through Taylor series expansion.Derivative in Newton's method was replaced to propose a new SPH iterative method for solving nonlinear equations. The advantage of this method is that it does not require any evaluation of derivatives, which overcame the shortcoming of Newton's method. Quadratically convergent of new method was provedand a variety of numerical examples were given to illustrate that the method has the same computationaleciency as the Newton's method.