The tap water driven McKibben muscle possesses several merits of the water hydraulic system, including high flexibility, low weight, and high power density. These aspects enable the application of this muscle system to mechanical systems that require high cleanliness. However, the muscle shows strong asymmetric hysteresis characteristics depending on the applied load, which blocks its effective application. This study presents an appropriate modelling of the hysteresis characteristics of the muscle using an asymmetric Bouc-Wen model along with a control strategy, based on the model predictive control with servomechanism (MPCS). Subsequently, an inverse optimisation is proposed by applying an adaptive model matching to make the compensated system match the prespecified predictor to reduce the time-consuming routine for obtaining proper weight matrices in the evaluation function of the model predictive control. The numerical simulation results show that the proposed approach works well, and easier controller tuning can be achieved.