A new type of self-centering confined masonry wall equipped with both unbounded tendons and external steel dampers was proposed. Its hysteresis behavior was studied through pseudo-static tests under cyclic loading, which focused on investigating the influence of the initial prestress of the tendon and the yield load of dampers on the energy dissipation capacity of the proposed wall. Based on the test results, a simplified numerical analysis model was established. It is showed that flag shape was a typical hysteresis curve of the wall. During the loading and unloading process, the wall specimen remained intact, and significant degradation of strength and stiffness was not observed. It is also found that the increase of the initial prestress in tendons led to the enhancement of the self-centering ability but the reduction of the energy dissipation capacity of the wall on the other hand, when the yield force of steel dampers increased, the energy dissipation capacity of the wall was improved, but some residual displacement occurred. Moreover, the numerical analysis results matched well with the test results, which indicate that the proposed numerical models can well capture the mechanical behavior of the wall.