Power-split transmission is considered as one of the major technologies for hybrid electric vehicles. It utilizes two electric motors and a power-split device (planetary gear sets) to make the engine speed independent from the vehicle speed, and in that way enables the engine operate in a high efficiency region under all driving cycles. Due to the difficulty of obtaining accurate engine and clutch/brake torques in real time and the difference of torque response characteristics between clutch/brake, engine and electric motors, the torque estimation and coordinated control method is of crucial importance to the drivability improvements. In this study, firstly, a detailed dynamic plant model of the power-split hybrid vehicle is established to analyze the operating modes and mode switch characteristics. Secondly, a real-time transmitted torque observer based on Kalman filter is implemented to acquire the torques in input and output shafts of the power-split transmission which are connected with the engine and main reducer respectively. Thirdly, a coordinated control strategy is developed to determine the desired engine and motor torques. The proposed control method consists of three objectives: 1. to make the engine speed tracking the target value by controlling the torques of engine and electric motors; 2. to ensure the vehicle dynamic performance by utilizing the electric motors to compensate the difference between desired and estimated transmitted torques; 3. to mitigate the vehicle vibration by using active damping control algorithm. The simulation results in MATLAB/Simulink demonstrate that, the developed control method effectively guarantees the engine operating range, meets the driver demands and improves the ride comfort during both steady mode and mode switch.