In this article, a new three-phase seven-level inverter is proposed with a new switching algorithm. This algorithm has eighteen switching steps. The switching algorithm is implemented on a topology, which consists of three legs and each leg has four switches. The switching frequency for six switches is the same as output wave frequency. The proposed algorithm results in lower switching losses, higher efficiency, and lower number of switches. This inverter has low cost and low volume, and is especially suitable for standalone applications. In addition, a modified pulsewidth modulation (PWM)-based version is proposed for eighteen-step switching algorithm to reduce the filter size and increase the controllability of the output waveform. Simulation and experimental results demonstrate good performance of the proposed inverter.