Acceptance sampling plans are useful tools to determine whether the submitted lots should be accepted or rejected. An efficient and economic sampling plan is very desirable for the high quality levels required by the production processes. The process capability index C_L is an important quality parameter to measure the product quality. Utilizing the relationship between the C_L index and the nonconforming rate, a repetitive group sampling (RGS) plan based on C_L index is developed in this paper when the quality characteristic follows the Weibull distribution. The optimal plan parameters of the proposed RGS plan are determined by satisfying the commonly used producer’s risk and consumer’s risk at the same time by minimizing the average sample number (ASN) and then tabulated for different combinations of acceptance quality level (AQL) and limiting quality level (LQL). The results show that the proposed plan has better performance than the single sampling plan in terms of ASN. Finally, the proposed RGS plan is illustrated with an industrial example.