The optimal reinsurance-investment strategy for an insurer with an exogenous liability is considered. Assume that the aim of the insurer is to maximize the expected exponential utility of the terminal wealth; the surplus process of the insurer follows a diffusion model while the risky assets' prices and the exogenous liability are governed by geometric Brownian motions. By employing the stochastic dynamic programming, the closed form of the optimal reinsuranceinvestment strategy and the optimal value function are derived under two cases: (i) the insurer can invest in a financial market and purchase proportional reinsurance or acquire new business, (ii) the insurer can invest in a financial market and purchase proportional reinsurance, but not acquire new business. Finally, a numerical example is given to show the impact of the exogenous liability and the market parameters on the optimal strategy.