Fundamentally, second-order model is the foundation of describing the dynamic characteristics of many mechanical and electrical systems. This paper investigates a parametric identification scheme for single degree-of-freedom second-order model in which the model parameters are subject to normal variation. By utilizing frequency response magnitude and phase angle measurements, we construct a linear-in-the-parameters model and build a related maximum likelihood estimator for both parametric means as well as variances. The validity of the approach is demonstrated through a collection of case analyses, and the results show considerable levels of accuracy in the presence of sufficient data.