The invention discloses a parallel self-adaptive grasping robot dexterous hand. The parallel self-adaptive grasping robot dexterous hand comprises a base and fingers. The fingers comprise the first finger, the second finger and the third finger. Each finger comprises a far-end finger rod and a near-end finger rod. The first finger is fixedly connected to the base. The second finger and the third finger can rotate around the central axis perpendicular to the base. In the dexterous hand grasping process, when the near-end finger rods do not make contact with an object, the far-end finger rods linearly and horizontally move to parallelly grasp the object, and the object also can be grasped in a self-adaptive envelope mode according to the different sizes and shapes of the object after the near-end finger rods make contact with the object. Meanwhile, the positions of the rotatable fingers can be adjusted in a large range, so that a plurality of grasping structure states are produced, and the capacity to grasp different shapes of objects is improved. The parallel self-adaptive grasping robot dexterous hand is ingenious in structural design, small in size, few in driver, capable of automatically adapting to different sizes and shapes of objects, high in grasping capacity, large in range, stable and reliable.