The conformability is yet a challenge for most soft robotic grippers due to the continuous motion and deformation of these machines under external force. Herein, inspired by the movement mechanism of human fingers, we propose a novel tendon-driven soft robotic finger with a preprogrammed bending configuration and a human finger like sequential motion that can be obtained by matching the stiffness gradient of the finger joints with three-dimensional (3D) printing technology. The contents of this article are organized as follows. First, the effect of the anisotropy caused by 3D printing filling direction on the mechanical property is investigated by tensile test. Then, kinematic, stiffness, and fingertip trajectory models are established to analyze the influence of the cross-section thickness and width on the bending and bearing capacity of the finger joint. Furthermore, several experiments are conducted on a self-built experimental platform to evaluate the advantages of sequential motion induced by stiffness gradients. Results reveal that soft robotic fingers with sequential motion show excellent conformability on the object surfaces with various curvatures and outperform nonsequential motion fingers with larger envelop range. Without changing motion trajectories of the fingertip, the deformability of the finger can be tuned by adjusting only the stiffness of the joint. Besides, a two-finger gripper is developed, which presents the capability of grasping objects with different shapes and weights in practical applications. The sequential motion mechanism proposed in this study shows promising potential in soft grippers and robotic design.