This paper proposes a parametric identification method for parallel Wiener systems. The linear dynamic parts of the Wiener system are modeled by a parametric rational function in the Laplace or z-domain. The static nonlinearity is represented by a linear combination of multiple-input single-output nonlinear basis functions. The identification method uses a three-step procedure to obtain initial estimates. In the first step, the frequency response function of the best linear approximation is estimated for different input excitation levels. In the second step, the power-dependent dynamics are decomposed over a number of parallel orthogonal branches. In the last step, the static nonlinearities are estimated using a linear least squares estimation. Furthermore, a nonlinear optimization method is implemented to refine the estimates. The method is illustrated on a simulation and a validation measurement example.