In the paper the Gerber-Shiu discounted penalty function has been studied in risk model, which the claim process is a compound Poisson-Geometric process and the defective renewal equation of the Gerber-Shiu discounted penalty function has been given. Through the above result the defective renewal equation about the ruin probability and the marginal distributions of the deficit at ruin have been deduced. Finally the Pollazek-Khinchin formula of ruin probability has been obtained using Laplace transform method and based on the Pollazek-Khinchin formula the express of ruin probability has been ob...