A variety of the multi-finger robot hands have been developed up to now. However, most of them have weak force at the fingertip. Some of the flexible robot hands also have weak force at the fingertip. Although the soft hand with pneumatic actuation can have strong driving force, their control precision is low. A flexible robot hand based on slider and rocker mechanism was designed. It had three fingers. In each finger, the fingertip and the middle phalange were realized through a slider and rocker mechanism for which the force of the fingertip was strengthened. The tendon transmission was used for the proximal phalange, which guaranteed the driving force. The springs were used for the motion of the fingertip and proximal phalange to avoid the hard contact at the object. The spring that drove the fingertip was soft for good flexibility at initial contact. The spring that drove the proximal phalange was moderately hard to guarantee the sufficient force. The fingertip can achieve strong force through the mechanic analysis and computation. The analysis was performed on how to determine the springs. The experiments on grasping different common objects showed that the proposed robot hand had good adaptability and grasping ability. The experimental results on grasping force tests proved that the proposed robot hand can grasp much heavier objects compared with the former robot hand also designed by our research group. It can grasp an object with the maximum weight of 1.71kg. The tests on the relationship between the normal force of the fingertip and rotational angle of the servo motor of the proximal phalange and the destruction tests on grasping some typical objects were performed. The results showed that the proposed robot hand had good flexibility. These performances indicated the usefulness of the proposed robot hand.