This paper presents an adaptive compliant multi-finger grasp approach control strategy based on based on a new interpretation of the virtual spatial spring framework, to improve the grasp performance for target objects with position errors. An n-finger virtual spatial spring frame is proposed to achieve the adaptive compliant grasp control. Two-finger grasp control based on a single virtual spring is tackled, and then extended to multi-finger grasp control. Virtual springs for self-collision avoidance among digits are constructed to form the complete adaptive compliant grasp control law. With the virtual-spring based adaptive compliant grasp approach control strategy, the first robot finger to experience unexpected impact remains in contact with the object, while the rest of the fingers are continuously, adaptively driven toward re-adjusted grasping positions by the virtual springs without the need for on-line replanning. Experimental results demonstrate effectiveness of the virtual-spring based grasp controller, and significantly larger position errors of the target object can be accommodated with the proposed adaptive compliant grasp control strategy.