This article presents a non-iterative method to identify a continuous-time Wiener model. The key idea is to describe the linear dynamics by a Laguerre expansion and approximate the static nonlinearity by an inverse polynomial function. The resulting least-squares estimator of the Laguerre and polynomial coefficients is thus obtainable in a non-iterative manner. To improve the estimation accuracy of both linear and nonlinear parts, an error criterion is developed to infer the proper values of the time-scaling factor and output reference value, which are crucial to the effectiveness of the Laguerre expansion and the polynomial function, respectively. The identified Wiener model can be easily employed to design a nonlinear controller for the Wiener process. It is demonstrated that the identification and control method is valid for a wide range of test conditions and process nonlinearities.