This paper presents an adaptive and compliant approach-to-grasp strategy for multi-finger robotic hands, to improve the performance of autonomous grasping when encountering object position uncertainties. With the proposed approach-to-grasp strategy, the first robot finger to experience unexpected impact would pause its movement in a compliant manner, and remains in contact with the object to minimize the unplanned motion of the target object. At the same time, the remainder of the fingers continuously, adaptively move toward re-adjusted grasping positions with respect to the first finger in contact with the object, without the need for on-line replanning or re-grasping. An adaptive grasp control strategy based on spatial virtual spring framework is proposed to achieve local (e.g. not resorting to the robotic arm) in-hand adjustments of the fingers not yet in contact. As such, these fingers can be adaptively driven to the adjusted desired position to accomplish the grasp. Experimental results demonstrate that significantly larger position errors with respect to the hand workspace can be accommodated with the proposed adaptive compliant grasp control strategy. As much as 391% increase in position error area coverage has been achieved. Finally, beyond the quantitative analysis, additional observations during the extensive experiment trials are discussed qualitatively, to help examine several open issues, and further understand the approach-to-grasp phases of the robot hand tasks.