In this paper, we consider a new risk model of compound Poisson-Geometric process which assumes that the insurance company receives the premium with a differentiable rate. By applying the differential argument method, a defective renewal equation of Gerber-Shiu discounted penalty function is obtained. Based on the results, the defective renewal equation of the ruin probability, the moments of the surplus immediately prior to ruin and the deficit at ruin have been deduced. By solving the differential equation, the inequality which the ruin probability satisfied have been obtained when the claim variable random belongs to the exponential distribution. Moreover, numerical analysis of the distribution is presented and some examples are given. Finally, we conclude that the impacts of the adjustment policy and the premium policy to the insurance company.