Single-phase solid-state transformers (SSTs) have the advantages of a compact structure, higher reliability, and multiple functions, and have been widely studied. However, bulky energy storage elements and inherent ripple power with double-grid frequency issues are the main disadvantages of conventional single-phase SSTs. This paper presents a single-phase matrix-type AC-AC SST eliminating ripple power with double-grid frequency. The presented SST consists of a line-frequency-commutated rectifier without bulky DC-link capacitors, an LLC resonant converter, a buck converter, and a line-frequency-commutated inverter. The LLC operates efficiently with a fixed voltage gain, and the buck converter provides a voltage regulation function. As a result, high conversion efficiency, high power density, and potentially high reliability are achieved. A 1 kW SST prototype is developed and tested to validate the feasibility and functionality of the proposed methods.