Summary: Positive-definite and skew-Hermitian splitting (PSS) method is an unconditionally convergent iterative method for solving large sparse non-Hermitian positive definite system of linear equations. By making use of PSS iteration as the inner solver of an inexact Newton method, we establish a class of inexact Newton-PSS methods for solving large sparse systems of nonlinear equations with positive-definite Jacobian matrices at the solution points. The local and semilocal convergence properties are analyzed under some proper assumptions. Numerical results are given to examine the feasibility and effectivity of inexact Newton-PSS methods.