This paper investigates an optimal reinsurance-investment problem with HARA utility. In order to avoid claim risks, the insurer is allowed to purchase reinsurance, and is assumed to invest in one risk-free asset and one risky asset whose instantaneous rate is governed by an Ornstein-Uhlenbeck (O-U) process, which could describe the features of bull and bear markets. Firstly, under the criterion of maximizing the expected HARA utility of the insurer's terminal wealth, the HJB equation for the value function is obtained by applying dynamic programming principle. Secondly, due to the complexity of the structure of HARA utility, we use Legendre transform to change the original HJB equation into its dual one, whose solution is easy to conjecture. Closed-form solution of optimal investment-reinsurance strategy is obtained by constructing the solution form of the dual equation and the variable change technique. Finally, some numerical simulations are presented to illustrate the impacts of model parameters on the optimal reinsurance-investment strategy.