Road construction work on poor subgrade in coastal, port, and reclamation sites is a traditional challenge for geotechnical engineers because of the typically very weak clayey soil in these domains. This research investigates the effects of adding a new green binder (Fa-RmLG), in different proportions and initial water contents, on the engineering properties of marine dredged clay (MDC) collected from Yeosu port, South Korea. The new green binder used is a combination of fly ash (Fa), phosphogypsum (G), lime (L), and red mud (Rm). In this study, five binder mixtures using different proportions of Fa, G, L, and Rm were blended into MDC with different water contents varying in a range of 1.2 to 2.0 times the liquid limit (LL) value. Tests of unconfined compressive strength, California bearing ratio, swelling, and shrinkage were performed on the stabilized MDC mixtures. As a result, large increases in the strength and bearing capacity as well as significant reductions of the swelling and shrinkage values of the stabilized MDC mixtures were recorded compared with unstabilized MDC. Scanning electric microscope and X-ray diffraction analyses were performed to observe the formation and presence of gels inside the stabilized MDC mixtures. Regarding environmental impact, the pH of the stabilized MDC mixtures did not increase above the corrosive limit (pH = 12.5) by the measured pH value. These results indicate that the new green binder can be used as an effective stabilizer for the stabilization of MDC in coastal road construction.