Fuel efficient power system for electric boat is provided. In starting a clutch is not activated if a drive shaft of an electric motor does not rotate at a predetermined speed, a power controller gradually increases a current output to the motor until the drive shaft rotates at the predetermined speed, the third clutch is activated to transmit rotation of the drive shaft to an electrical generator, and the activated generator charges one low rechargeable battery. In response to activating a first clutch rotation of the drive shaft is transmitted to a first shaft, a bevel gear clutch is activated to transmit rotation of the first shaft to a propeller via a reduction gear. In response to moving the boat the first clutch is disengaged and a second clutch is engaged for transmitting rotation of the drive shaft to the second shaft, and a gearbox for increasing propeller speed.