In this paper, we present the implementation of a real-time LTE-NOMA baseband receiver on a software-defined radio (SDR) platform. The platform consists of a PC with a high-performance GPU and several universal software radio peripherals (USRPs) that are controlled by the USRP hardware driver (UHD). For portability and support of high data parallelism on the baseband modem, the software baseband receiver was designed in the Open computing language (OpenCL). Finally, the transceiver was validated via real-time demonstration showing successful over-the-air LTE-NOMA signal transmission and data reception for two intended users, each with two spatial streams, at 15.36 MHz sampling rate and several power ratios between two users.