A novel stochastic channel impulse response matrix (CIRM) model for massive multiple input multiple output (MI-MO) channels is proposed in this papen Under the framework of this proposed model, the CIRM can be modeled as a sum of couplings between the steering vectors at the base station (BS) end and the eigenbases at the mobile station (MS) side. The fading of the coupling between the steering vector and the eigenbase is modeled as Nakagami distribution. Furthermore, the closed form of the capacity is derived based on the proposed framework. Compared with the traditional Weibchselberger model, the proposed model has lower complexity. To validate the proposed model, extensive massive MIMO channel measurements are carried out in an indoor environment The results show that the new model provides a better fit to the measured results than Weibchselberger model. Finally, the closed form and PDF are validated by Monte Carlo realizations of the proposed model. This CIRM model can be used for massive MIMO design in future fifth-generation communication system design.