We studied the low-temperature electrical properties of the two-dimensional organic conductor Љ-͑BEDT-TTF͒ 2 AuBr 2 , whose electronic structure is similar to that of the pressure-induced superconductor Љ-͑DODHT͒ 2 PF 6 having a charge-ordered transition at 255 K at ambient pressure. We found that the ground state of Љ-͑BEDT-TTF͒ 2 AuBr 2 at ambient pressure has a charge-density-wave phase below 6.5 K accompanied by x-ray superlattice spots. We also discovered superconductivity in the vicinity of the charge-densitywave phase by applying uniaxial strain. Based on the obtained results, we propose a unified electronic phase diagram that suggests the relationships among the charge-ordered insulating state, the superconducting phase, and the charge-density-wave phase in Љ-type organic conductors. The phase diagram shows that the superconducting phase is located near the charge-density-wave phase, which suggests that spin fluctuations play a minor role in the mechanism of the superconductivity and sheds light on the possibility of charge-fluctuationmediated superconductivity in this type of organic conductor.