In this paper, a cooperative single-carrier transmission scheme considering a distributed quasi-orthogonal space-frequency block code (QOSFBC) that provides improved peak-to-average power ratio (PAPR) performance is constructed for uplink communications. Focused on reducing the size and computational complexity, the source node, i.e., the mobile devices, is equipped with two transmit antennas, while only one antenna is required at the relay node in order to collaboratively generate a distributed QOSFBC signal using four transmit antennas. To achieve full diversity, a phase rotation strategy is proposed at the relay node. In addition, since single-carrier schemes considering SFBCs re-permute the spectral components of the transmitted signal and induce high PAPR value, a modified SFBC coding technique is proposed that allows the high-PAPR problem to be mitigated. Consequently, the designed distributed single-carrier frequency-division multiple access (SC-FDMA) QOSFBC scheme is able to provide full transmit diversity over frequency-selective fading channels, with a lower PAPR value on mobile devices when compared with a conventional SC-FDMA QOSFBC scheme.