Abstract: In this paper, the surplus of an insurance company is governed by a jump-diffusion process, and it can be invested in a financial market with one risk-free asset and N risky assets. The parameters of surplus process and the asset price processes depend on the regime of the financial market, which is modeled by an observable finite-state continuous-time Markov chain. To maximize the terminal utility, we focus on finding optimal investment strategy and solve it by using the HJB equation. Explicit expression for optimal strategy and the corresponding objective function are presented when the company has an exponential utility function, some interesting economic interpretations are involved. Some known results of Browne (1995) and Yang and Zhang (2005) are extended.