Abstract：The method of credibility theory plays a critical role in various research areas of actuarial science. Among others, the hypothetical mean and process variance are two quantities that convey crucial information to insurance companies when determining premiums for the insureds. The classical simple Bühlmann model charges premiums by applying a linear combination of the mean of past claims and the population mean, which is proven the best estimator of the hypothetical mean under the mean squared loss criterion. Enlightened by the prestigious mean-variance premium principle, we propose a credibility approach to estimating the linear combination of hypothetical mean and process variance under the mean quadratic loss function. It is found that our proposed estimator consists of several parts involved with the linear form of observations and their quadratic terms, as well as some quantities representing population information. Several numerical illustrations are carried out to demonstrate the performance of the estimator.  Meanwhile, a spin-off result is found and utilized to compare with the classical simple Bühlmann model and the q-credibility model. The non-parametric estimators of structural quantities are also provided for ease of its practical usage, yielding the empirical credibility estimator.