An apparatus for discharging exhaust gas of a vehicle may include an exhaust port forming a first confluence part at which at least two runners among runners of an exhaust manifold connected with a cylinder are joined, and a second confluence part at which the remaining runners are joined, and a connector member having an inlet port through which exhaust gas discharged through the exhaust port is introduced, and having a partition which is formed toward the exhaust port in the inlet port so as to partition the first confluence part and the second confluence part.