This work presents a new discrete-time adaptive-predictive control algorithm for a system with force disturbance and input delay. This scenario is representative of a mechatronic device for percutaneous intervention with pneumatic actuation and long supply lines which is controlled remotely in the presence of an unknown external force resulting from needle-tissue interaction or gravity. The ultimate goal of this research is the robotic-assisted percutaneous intervention of the liver under Magnetic Resonance Imaging (MRI) guidance. Since the control algorithm is intended for a digital microcontroller, it is presented in the discrete-time form. The controller design is illustrated for a 1 degree-of-freedom system and is conducted with a modular approach combining position control, adaptive disturbance compensation, and predictive control. The controller stability is analyzed and the effect of the input delay and of the tuning parameters is discussed. The controller performance is assessed with simulations considering a disturbance representative of needle insertion forces. The results indicate that the adaptive-predictive controller is effective in the presence of a variable disturbance and of a known or variable input delay.