A power transmission control device for a vehicle, which is to be applied to a vehicle comprising an internal combustion engine and an electric motor as power sources, the power transmission control device comprising: a multiple gear ratio transmission including an input shaft for inputting a power from an output shaft of the internal combustion engine and an output shaft for outputting a power to drive wheels of the vehicle, and having a plurality of predetermined gear positions different in speed reduction ratio, which is a ratio of a rotation speed of the input shaft to a rotation speed of the output shaft, the output shaft of the multiple gear ratio transmission inputting a power from an output shaft of the electric motor without Intermediation of a power transmission line between the input shaft and the output shaft of the multiple gear ratio transmission; a clutch interposed between the output shaft of the internal combustion engine and the input shaft of the multiple gear ratio transmission, the clutch being capable of adjusting a clutch torque, which is a maximum value of a torque transmittable by the clutch; a first actuator for controlling the clutch to adjust the clutch torque; a second actuator for controlling the multiple gear ratio transmission to change a gear position to be realized out of the plurality of gear positions; and control means for controlling, based on a travel state of the vehicle, an internal-combustion-engine driving torque, which is a driving torque of the output shaft of the internal combustion engine, an electric-motor driving torque, which is a driving torque of the output shaft of the electric motor, the first actuator, and the second actuator, the control means being configured to selectively realize, based on the travel state of the vehicle, an electric-motor travel mode for traveling by using only the electric-motor driving torque in a state in which the clutch torque is maintained to zero, and an internal-combustion-engine travel mode for traveling by using one of only the internal-combustion-engine driving torque and both the internal-combustion-engine driving torque and the electric-motor driving torque in a state in which the clutch torque is adjusted to a value larger than zero, characterized in that the control means is configured, in a state in which the electric-motor travel mode is selected, to change the gear position to be realized depending on the travel state of the vehicle when it is determined that a speed of the vehicle is higher than a predetermined speed, and to maintain the gear position to be realized to a current gear position independently of the travel state of the vehicle when it is determined that the speed of the vehicle is equal to or lower than the predetermined speed. a multiple gear ratio transmission including an input shaft for inputting a power from an output shaft of the internal combustion engine and an output shaft for outputting a power to drive wheels of the vehicle, and having a plurality of predetermined gear positions different in speed reduction ratio, which is a ratio of a rotation speed of the input shaft to a rotation speed of the output shaft, the output shaft of the multiple gear ratio transmission inputting a power from an output shaft of the electric motor without Intermediation of a power transmission line between the input shaft and the output shaft of the multiple gear ratio transmission; a clutch interposed between the output shaft of the internal combustion engine and the input shaft of the multiple gear ratio transmission, the clutch being capable of adjusting a clutch torque, which is a maximum value of a torque transmittable by the clutch; a first actuator for controlling the clutch to adjust the clutch torque; a second actuator for controlling the multiple gear ratio transmission to change a gear position to be realized out of the plurality of gear positions; and control means for controlling, based on a travel state of the vehicle, an internal-combustion-engine driving torque, which is a driving torque of the output shaft of the internal combustion engine, an electric-motor driving torque, which is a driving torque of the output shaft of the electric motor, the first actuator, and the second actuator, the control means being configured to selectively realize, based on the travel state of the vehicle, an electric-motor travel mode for traveling by using only the electric-motor driving torque in a state in which the clutch torque is maintained to zero, and an internal-combustion-engine travel mode for traveling by using one of only the internal-combustion-engine driving torque and both the internal-combustion-engine driving torque and the electric-motor driving torque in a state in which the clutch torque is adjusted to a value larger than zero, characterized in that the control means is configured, in a state in which the electric-motor travel mode is selected, to change the gear position to be realized depending on the travel state of the vehicle when it is determined that a speed of the vehicle is higher than a predetermined speed, and to maintain the gear position to be realized to a current gear position independently of the travel state of the vehicle when it is determined that the speed of the vehicle is equal to or lower than the predetermined speed.