A traveling mode switching controller of a hybrid electric vehicle that has an engine for actuating drive wheels of a vehicle and a generator, a drive battery which can be charged when supplied with electric power from the generator, a drive motor that actuates the drive wheels by electric power supplied from the drive battery or electric power supplied from the generator, and a clutch which connects and disconnects driving force transmitted from the engine to the drive wheels and that travels while switching among a first traveling mode in which the clutch is released and the engine is deactivated and in which the drive wheels are actuated by activating the drive motor by use of the electric power supplied from the drive battery; a second traveling mode in which the clutch is released, in which the generator is actuated by the engine to generate electric power, and in which the drive motor are activated by the electric power to actuate the drive wheels; and a third traveling mode in which the clutch is connected and in which the drive wheels are actuated by the engine, the traveling mode switching controller comprising: a velocity detection unit for detecting a traveling velocity of the vehicle; a state-of-charge detection unit for detecting a state of charge of the drive battery; and a switching control unit for selectively switching among the first traveling mode, the second traveling mode, and the third traveling mode on the basis of the traveling velocity of the vehicle and the state of charge of the drive battery, wherein the switching control unit performs switching between the second traveling mode and the third traveling mode at a first velocity (A, A) when the state of charge is less than a first state of charge, and switching between the first traveling mode and the third traveling mode at a predetermined velocity (C, C which is higher than the first velocity (A, A) when the state of charge is the first state of charge or more, characterized in that the controller further comprising request output detection unit for detecting a request output that is required of the vehicle, wherein the switching control unit performs, when the state of charge is higher than the first state of charge, switching between the second traveling mode and the third traveling mode at a second velocity (B, B) which is higher than the first velocity (A, A) on occasion when the request output is a predetermined request output or more, and switching between the first traveling mode and the third traveling mode at a third velocity (C, C) which is higher than the second velocity (B, B) on occasion when the request output is less than the predetermined request output. a velocity detection unit for detecting a traveling velocity of the vehicle; a state-of-charge detection unit for detecting a state of charge of the drive battery; and a switching control unit for selectively switching among the first traveling mode, the second traveling mode, and the third traveling mode on the basis of the traveling velocity of the vehicle and the state of charge of the drive battery, wherein the switching control unit performs switching between the second traveling mode and the third traveling mode at a first velocity (A, A) when the state of charge is less than a first state of charge, and switching between the first traveling mode and the third traveling mode at a predetermined velocity (C, C which is higher than the first velocity (A, A) when the state of charge is the first state of charge or more, switching between the second traveling mode and the third traveling mode at a first velocity (A, A) when the state of charge is less than a first state of charge, and switching between the first traveling mode and the third traveling mode at a predetermined velocity (C, C which is higher than the first velocity (A, A) when the state of charge is the first state of charge or more, characterized in that the controller further comprising request output detection unit for detecting a request output that is required of the vehicle, wherein the switching control unit performs, when the state of charge is higher than the first state of charge, switching between the second traveling mode and the third traveling mode at a second velocity (B, B) which is higher than the first velocity (A, A) on occasion when the request output is a predetermined request output or more, and switching between the first traveling mode and the third traveling mode at a third velocity (C, C) which is higher than the second velocity (B, B) on occasion when the request output is less than the predetermined request output. switching between the second traveling mode and the third traveling mode at a second velocity (B, B) which is higher than the first velocity (A, A) on occasion when the request output is a predetermined request output or more, and switching between the first traveling mode and the third traveling mode at a third velocity (C, C) which is higher than the second velocity (B, B) on occasion when the request output is less than the predetermined request output.