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In this paper, we study the optimal reinsurance and investment problem for a class of jump-diffusion model, where the diffusion term represents the additional claims (i.e. A-C case). The insurer can purchase proportional reinsurance while allowing she/he to invest in a risk-free asset and a risky asset. The price process of the risky asset is driven by geometric Lévy process with dividend payouts. Applying stochastic control theory, the corresponding Hamilton–Jacobi–Bellman equation is established and the optimal reinsurance-investment strategies to maximize the expected exponential utility of terminal wealth are also established. Finally, the optimal strategies are analysed by the numerical simulation.