We propose a new parameter estimation method for Hammerstein-Wiener-type processes composed of the input-output nonlinear static functions and a linear dynamic subsystem. A special test signal is designed to separate the identification problems of the linear dynamic subsystem and the output nonlinear static function from that of the input nonlinear static function. Then, the system identification procedure can be significantly simplified: the identification problems of the linear dynamic subsystem and the output nonlinear static function can be solved independently without considering the input nonlinear static function, and the model parameters of the input nonlinear static function can also be estimated analytically without any iterative nonlinear optimization. Furthermore, we develop a new estimation algorithm to identify the linear dynamic subsystem and the output nonlinear static function more efficiently. This algorithm does not need to initialize the model parameters of the output nonlinear static function and reduces the searching space in the iterative nonlinear optimization problem, resulting in more robust and faster convergence and easier initialization in the nonlinear optimization compared to previous approaches.