This paper deals with the optimal dividend payment and capital injection problem for the classical risk model perturbed by diffusion. The objective of the corporation is to maximize the discounted dividend payments minus the penalized discounted capital injections until ruin. The problem is formulated in a stochastic control framework. By solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation, we obtain the optimal dividend and capital injection strategy of the problem. Under some suitable assumptions, the optimal dividend strategy prescribes to company using a barrier strategy and paying no dividends when the reserve is below some critical level $b$ and paying out everything that exceeds $b$. The optimal injection strategy is described by the optimal lower and upper injection barriers. We solve this problem explicitly in the case of exponential claim amount distributions.

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