This letter considers an active reconfigurable intelligent surface (RIS)-aided multi-user uplink massive multipleinput multiple-output (MIMO) system with low-resolution analog-to-digital converters (ADCs). The letter derives the closedform approximate expression for the sum achievable rate (AR), where the maximum ratio combination (MRC) processing and low-resolution ADCs are applied at the base station. The system performance is analyzed, and a genetic algorithm (GA)-based method is proposed to optimize the RIS's phase shifts for enhancing the system performance. Numerical results verify the accuracy of the derivations, and demonstrate that the active RIS has an evident performance gain over the passive RIS.