The 'rabbet-unbonded horizontal connection' (RUHC) is a new connection form of precast shear wall. This study conducted a low-cycle repeated loading test on three RUHC walls to investigate the hysteretic performance of the walls with the 'axial compression ratio' and 'unbonded level' as the main variables and the results showed that the above two parameters remarkably affected the seismic performance of RUHC walls. Based on the analysis of test skeleton and hysteresis curve characteristic, the influence of parameters such as axial compression ratio and unbonded level on the load and displacement during the loading process was analyzed. The theoretical values of yield, peak and limit points were calculated, and the skeleton curve model was proposed. Moreover, the unloading stiffness formula was proposed by the non-linear relation of dimensionless parameters and Matlab software fitting, and the hysteresis rule model was established. Finally, a three-fold-linear restoring force model of RUHC walls composed of the theoretical skeleton curve and hysteresis rule was established and verified. This model provides an effective prediction for the hysteresis characteristics and a theoretical basis for conducting elastic-plastic analysis of RUHC structures.