Multifingered hand dexterous manipulation is quite challenging in the domain of robotics. One remaining issue is how to achieve compliant behaviors. In this work, we propose a human-in-the-loop learning-control approach for acquiring compliant grasping and manipulation skills of a multifinger robot hand. This approach takes the depth image of the human hand as input and generates the desired force commands for the robot. The markerless vision-based teleoperation system is used for the task demonstration, and an end-to-end neural network model (i.e., TeachNet) is trained to map the pose of the human hand to the joint angles of the robot hand in real-time. To endow the robot hand with compliant human-like behaviors, an adaptive force control strategy is designed to predict the desired force control commands based on the pose difference between the robot hand and the human hand during the demonstration. The force controller is derived from a computational model of the biomimetic control strategy in human motor learning, which allows adapting the control variables (impedance and feedforward force) online during the execution of the reference joint angles. The simultaneous adaptation of the impedance and feedforward profiles enables the robot to interact with the environment compliantly. Our approach has been verified in both simulation and real-world task scenarios based on a multifingered robot hand, that is, the Shadow Hand, and has shown more reliable performances than the current widely used position control mode for obtaining compliant grasping and manipulation behaviors.