A novel compound power-split hybrid transmission based on a modified Ravigneaux gear set is presented. The equivalent lever diagrams are used to investigate the electric operating modes for the hybrid powertrain, and then its dynamic and kinematic characteristics as well as efficiency characteristics are described in equations. A brake clutch mounted on the carrier shaft is proposed to enhance the electric driving efficiency for the hybrid transmission. Three types of electric operating mode are analyzed by the simplified combined lever diagrams and the system efficiency and torque characteristics for these electric operating modes are compared. A major influence on output torque of the hybrid transmission derived from the torque capability of motors and brake clutch is depicted. A control strategy for electric operating modes is discussed, and a transient optimization method is implemented to find the optimum selection of motors and the optimal brake torque of brake clutch for the hybrid powertrain. To evaluate the electrical economy of a hybrid car equipped with this hybrid transmission, a forward powertrain simulation model is developed. The simulations show that the proposed control strategy can improve the efficiency of the powertrain and demonstrate lower electricity consumptions than the corresponding vehicle equipped the hybrid transmission without a brake clutch.