The Gauss-Newton method is widely used for solving the least-square problems. In this work, the relationship between the parametrization of the inverse problem and the convergence rate of the Gauss-Newton method is studied. With different parametrization, the inverse problem shows different nonlinearity, which we characterized by nonlinearity constant and degree of nonlinearity. A convergence rate in terms of the nonlinearity is obtained and applications to nonlinear parameter identification problems are discussed. Numerical examples are given to demonstrate the effectiveness of the procedure.