Because of the crucial importance of the group decoding techniques to achieve higher data rates, and also since the massive MIMO expected to be a promising key 5G wireless technology, we aim in this paper to consider the problem of formulating the achieved capacity of the massive MIMO optimal successive group decoding (OSGD) system. To the best of the authors knowledge there is neither exact nor approximate closed-form expression describes the achieved capacity of the massive MIMO OSGD system, Therefore, in this paper we obtain a simple closed-form expression allows for tight approximation for the achieved capacity of the massive MIMO OSGD system. In addition to that we produce an accurate approximation formula describes the rate outage probability of this system. Numerical results is used to show the validation of the proposed formulas.