Acceptance sampling is an important tool for pressuring a producer to increase the quality of his or her products for consumers’ use. In this paper, a group acceptance sampling plan is developed in which the number of nonconforming items follows a Poisson model and the fraction nonconforming has a gamma prior. The methodology and tables are presented for the design of the proposed plan. The design parameters of the proposed plan are determined using the two-point approach on the operating characteristic curve such that the specified producer’s and consumer’s risks should be satisfied. The results are also explained with examples.