This paper presents the analysis and design of a cyclo-active-bridge (CAB) inverter for single-stage three-phase grid interface. The CAB inverter is an integration of three single-phase dual-active-bridge (DAB) converters and three cyclo converters, featuring individual phase shift and single-stage operation for high efficiency and fast dynamics. The topology utilizes high-frequency ac transformer links to eliminate bulky dc-link capacitors and filter inductors while achieving isolation and bidirectional power flow for the system. The dc-side of the inverter comprises three half bridges whose switched nodes are connected in a delta configuration. The ac-side of the inverter includes three half-bridge cycloconverters, each providing independent ac outputs. The output power of each phase is regulated through phase-shifting the primary and secondary sides with decoupled power flow in the three phases, enabling a simplified control scheme and enhanced system flexibility. An experimental prototype with a 48-V dc input, three-phase 240-Vrms ac outputs, and 600-W total output power has been developed and tested. Experimental results verified the functions and efficacy of the CAB inverter.