The present disclosure provides a method of controlling braking of an electric vehicle in which friction braking force generated by a friction braking unit is applied to front wheels and regenerative braking force generated by a motor is applied to rear wheels includes: determining driver's request braking force by a controller based on a driver's braking-input value; detecting driving information and state information of the vehicle by a detection unit; and determining a braking mode of the vehicle that satisfies the driver's request braking force by the controller based on the detected information and information of running state of the vehicle obtained from the detected information. In addition, the present disclosure provides a system of controlling braking of an electric vehicle.