A method is proposed to identify the model parameters of a stable, critically damped second-order plus time delay system. The method uses a step response of the closed-loop system using a PID controller. The two dominant poles of the closed-loop model were obtained using the step response. The process gain was calculated using the steady-state deviation values of the output and the input variable of the process. Using the identified dominant poles in the derived closed-loop characteristic equations, the relevant two nonlinear algebraic equations were derived to calculate the process delay and time constant. Three simulation examples were considered to show the effectiveness of the proposed method. The open-loop and as well as the closed-loop responses of the process were compared with those of the identified model and of the controller design based on the models. A significant improvement was obtained in the performance of the critically damped SOPTD model over that of the FOPTD model. The identified model parameters by the present method were compared with those of the relay auto-tuning method. A simulation study on a nonlinear bio reactor is also reported. © Taylor & Francis Group, LLC.