QR decomposition based near maximum likelihood (ML) block detection significantly improves the transmission performance of uplink single-carrier (SC) multi-user multiple-input multiple-output (MU-MIMO). Hybrid automatic repeat request (HARQ) is an indispensable error control technique for high quality packet data transmission. The achievable diversity gain of HARQ depends on the packet combining strategy. In uplink MU-MIMO HARQ, received signal may consist of new packets and retransmitted packets as retransmission for each user acts independently. In this paper, a recursive QR packet combining scheme suitable for uplink SC MU-MIMO HARQ is proposed, which takes into account the number of retransmissions for each user in the detection order. The proposed scheme helps reduce the computational complexity and storage requirement significantly. Moreover, it improves the packet error rate (PER) performance significantly over the conventional bit-level log likelihood ratio (LLR) packet combining, as shown by our computer simulation results.