This paper extends the model and analysis in that of Lin, Tan and Yang[Pricing annuity guarantees under a regime-switching model.North American Actuarial Journal 13(3) (2009), 316-332.].We assume that the financial market has a regimeswitching jump-diffusion model and the mortality satisfies Levy process.We price the point-to-point and annual reset EIAs by Esscher transform method under Mertons assumption and minimal martingale measure method.