This paper studies the parameter estimation problem for a class of separable nonlinear models, i.e., the RBF-ARX models. By exploiting the parameter separability property inherent in the RBF-ARX models, two gradient-based iterative sub-algorithms are derived to individually estimate the linear and nonlinear parameters based on the iterative search. Then a decomposition coordination-based iterative algorithm is proposed by integrating the sub-algorithms, which realizes high-precision iterative identification of all parameters. The effectiveness of the proposed algorithm is verified by a simulation example.