In this paper, we propose a uplink (UL) non-orthogonal multiple access (NOMA) systems equipped with multiple antennas to enhance the sum capacity of UL. In the proposed UL NOMA system, a base station (BS) with N antennas can support 2N users by sharing the space resource. However, sharing the space resource leads to interference between users. Therefore, to mitigate the interference and improve the sum capacity, we additionally propose a set selection algorithm and power control scheme. The set selection algorithm, which selects 2N users based on orthogonality and gain-difference between their channels, reduces the interference between users. Furthermore, the power control scheme can maximize the sum capacity with ensuring minimum target rate. Numerical results show that the proposed system improves the sum capacity over that of the conventional orthogonal multiple access (OMA) system.