The authors have continuously studied buckling-restrained braces using steel mortar planks (BRBSM). The performance of energy absorption and fatigue against cyclic loading has been evaluated. Although past studies have clarified the structural performance of BRBSM as single member, it is necessary to study not only the performance of BRBSM as single member but also the performance of BRBSM installed in a building structure. In this paper, a frame model of mid-rise steel structure with BRBSM subjected to earthquake motions with various characteristics is analyzed. Comparing the results of the analysis and the past tests, the seismic behavior of a structure is discussed. Especially, the seismic performance of BRBSM installed in the building structure is evaluated. In addition, the seismic performance of two types of BRBSM; basic and developed high-performance types, is compared and evaluated about cumulative plastic strain energy ratio and cumulative fatigue. As a result, the performance capacities of the both types of BRBSM exceed the required values of BRBSM under severe earthquake motions about cumulative plastic strain energy ratio and cumulative fatigue. The basic-type BRBSM has the fatigue capacity against 2 to 5 times severe earthquake motions. The required values of high-performance-type BRBSM are about a half of accumulated fatigue capacity compared with the basic-type one. The high-performance-type BRBSM is applicable against quite many cyclic loadings of low strain amplitude, and able to be used for long-term service.