Massive MIMO has become a key technology to the next wireless communication generation for its improvement in data rate, link reliability and power consumption; however, these benefits come at the cost of enormous data quantity, especially in the data detection of Massive MIMO uplink. In this paper, we propose a novel matrix inversion to balance the computational complexity and performance by providing selection of the 2-terms Neumann series approximation and the LDL decomposition matrix inversion methods according to different dimensions of the channel matrix. To reduce the hardware resource for two inversion algorithms and execute tasks efficiently, we consider the reconfigurable implementation for its flexibility and high-power efficiency. The implementation results are given by using our Reconfigurable Computing System for various antenna configurations. With this reconfigurable implementation, the throughput can achieve 93.8Mb/s, 130.4Mb/s, 82.2Mb/s and 107.1Mb/s for a 14×4 , 32×4 , 64×8 and 128× 8 system respectively, which are chose to even better than few implementations for high dimension problems.