Generic Model Control (GMC) is a control algorithm capable of using nonlinear process model directly. Parameters in GMC controllers are easily tuned, and measurable disturbances can be compensated effectively. However, the existence of large modeling errors and unmeasurable disturbances will make the performance of GMC deteriorate. In this paper, based on the theory of Strong Tracking Filter (STF), a new approach to Adaptive Generic Model Control (AGMC) is proposed. Two AGMC schemes are developed. The first is a parameter-estimation-based AGMC. After introducing a new concept of Input Equivalent Disturbance (IED), another AGMC scheme called IED-estimation-based AGMC is further proposed. The unmeasurable disturbance and structural process/model mismatches can be effectively overcome by the second AGMC scheme. The laboratory experimental results on a three-tank-system demonstrate the effectiveness of the proposed AGMC approach.