An engine clutch control apparatus of a vehicle including a transmission without a R-shift stage gear may include an engine clutch, a controller which determines whether an engine reverse rotation entry is possible for driving in reverse according to a failure diagnosis information of the engine clutch and executes a reverse rotation driving control according to the determination result, and a drive motor for reversely rotating the transmission according the reverse rotation driving control. The controller in the engine clutch control apparatus includes an engine reverse rotation entry possibility determining module and an engine exhaust gas forced discharge control module.