A matrix-type back-to-back converter (MT-BBC) with single-arm current injection, consisting of a three-phase rectifier with a small film dc-link capacitor and a three-phase inverter, is proposed in this paper. A clamped modulation strategy is applied to the rectifier, which is featured by only one high-frequency switching bridge arm, reduced switching losses, and enhanced input reactive power control range. By controlling and injecting the quasi-third harmonic current into the phase with a high-frequency switching bridge arm of the rectifier, sinusoidal input currents and controllable input power factor are achieved. A carrier modulation strategy with variable carrier is applied to the inverter to compensate for the time-varying six-pulse dc-link voltage. The presented converter inherits the advantages of both the conventional voltage-source back-to-back converter (V-BBC) and the matrix converter (MC) including simple main circuit structure, sinusoidal inputs and outputs, bidirectional power flow capability, potentially high power density, high reliability, high efficiency, and direct ac-ac conversion. Additionally, the input reactive power control range is extended significantly. The effectiveness of the proposed methods is verified by a 6-kW experimental prototype.