This paper proposes a new approach to modeling and compensating for a rate-independent hysteresis of a piezoactuator. The model—namely, congruency-based hysteresis—is developed based on two very important characteristics of the hysteresis. These are congruency and wipe-out. The proposed approach consists of two branches for cases of monotonic increase and monotonic decrease of input excitation. In order to realize this model, datasets of first-order minor-loop values should be determined in advance. This can be done using the adaptive neuron fuzzy system (ANFIS) technique and experimental data. With this technique, an input-output relationship of first-order minor-loop values is estimated effectively. In addition, the ANFIS technique is also used in constructing datasets of inverse first-order minor-loop values, which are essential parts of a congruency-based hysteresis compensator. Several experiments in modeling and open-loop control are conducted to show the effectiveness of the proposed approach. In addition, a comparative work between the proposed approach and one of previous works is undertaken to demonstrate the benefit of the proposed method.