In the past decades, the Tb3Ga5O12crystal has been market-dominating for visible–near-infrared Faraday applications. However, its relatively low Verdet constant as well as heavy volatilization of Ga2O3during growth makes it challenging to meet the continuous development of advanced lasers. In this work, a novel Tb3Al3Ga2O12crystal is designed and studied for the first time. We demonstrated that the Tb3Al3Ga2O12crystal possesses a better visible transparency, a higher thermal conductivity, and a larger Verdet constant compared with the Tb3Ga5O12crystal. Moreover, due to the great reduction of Ga content, it is more capable of fabricating large-size low-cost single crystals. Hence, Tb3Al3Ga2O12is an extremely potential material for Faraday applications in the visible–near-infrared range.