An apparatus for controlling a start of an engine of a hybrid vehicle is provided to prevent a torque change generated in the start of the engine from being transferred to a driving wheel by performing a slip connection of a second clutch while the engine is cranked by a gradual connection of a first clutch. An engine(1) and a motor/generator(5) are power sources. A first clutch(6) is installed between the engine(1) and the motor/generator(5) and changes the transfer torque quantity between the engine(1) and the motor/generator(5). A second clutch(7) is arranged between the motor/generator(5) and a driving wheel and changes the transfer torque quantity between the driving wheel and the motor/generator(5). A control apparatus controls the engine(1), the motor/generator(5), the first clutch(6), and the second clutch(7). The control apparatus selects an electrical driving mode in which a vehicle is driven by power of the motor/generator(5) by releasing the first clutch(6) and connecting the second clutch(7), or a hybrid driving mode in which the vehicle is driven by power of the engine(1) and the motor/generator(5) by connecting the first and second clutches(6,7). The control apparatus starts the engine(1) by a drag torque of the first clutch(6) through a connection of the first clutch(6) while the electrical driving mode is switched to the hybrid driving mode in a driving process. A second clutch connection control unit slip-connects the second clutch(7) to prevent a transfer torque change of the first clutch(6) from being transferred to the driving wheel. A motor/generator control unit(22) controls the motor/generator(5) to maintain a slip connection of the second clutch(7) in case that the second clutch(7) is slip-connected by the second clutch connection control unit.