While human-like series passive compliance has been used in previous robotic hand designs, little attention has been paid to parallel passive compliance due to the lack of understanding of its importance in grasping and manipulation. In this paper, we present a novel design of compliant finger inspired by biomechanical features and functionality of human hands. We develop a human-like compact joint by optimizing the geometry of a compliant material and mechanical elements. The joint exhibits a passive double exponential torque matching human-like compliance. We implement the compliant joint into a robotic finger design with human-like tendon routings. We carry out a series of experiments on the finger design with an open-loop control strategy in grasping and manipulation. The results show that the fingers perform reliable grasping and manipulation without feedback. We validate the trajectory tracking with a motion capture system. The human-like compliant fingers follow the desired trajectories with small errors (less than 1 cm). The innovative finger design realizes the human-like hand passive properties and achieves human-like grasping capability.