In this paper, we introduce a modified Chebyshev-like's method with order four and study the semilocal convergence of the method by using majorizing functions for solving nonlinear equations in Banach spaces. We prove an existence-uniqueness theorem and give a priori error bounds which demonstrates the R-order of the method. Moveover, the local convergence of this method is also analyzed. Finally, numerical application on nonlinear integral equations is given to show our approach.