Abstract: This paper studies an optimal investment and reinsurance problem in which the interest rate is driven by the Vasicek process, the surplus process is governed by a diffusion approximation model and two dependent classes of insurance business correlated through a common shock component are considered. The objective of the insurer is to minimize the variance of terminal wealth for a given terminal expected wealth. By using the stochastic linear-quadratic (LQ) control theory and the corresponding Hamilton-Jacobi-Bellman (HJB) equation, we obtain the explicit expressions for the value function, and the optimal investment and reinsurance strategies. Furthermore, the efficient strategies and efficient frontier are derived explicitly. Finally, some examples are given to show the influence of model parameters on the optimal investment and reinsurance strategies.