Perforated Yielding Shear Device-Rubber Bearing (PYSDRB) recently proposed by the author is a new base Isolation to reduce the seismic vibration. This paper tried to evaluate the seismic behavior of the steel moment frame with PYSDRB. The First 3, 8, and 12 story frames were designed with Lead Rubber Bearing (LRB), and then because of the restriction on the PYSDRB displacement, by removing the lead core of the LRB, a suitable pattern is proposed for the design of the shear plates. The base shear and the story drift in the fixed-base frames, frames with LRB-1 (high target displacement), LRB-2 (low target displacement), and PYSDRB under 7 earthquakes were compared. The base shear reduction rate of the 3, 8, and 12-story frames with PYSDRB were about 39%, 37%, and 35% respectively. This base shear reduction rate was acceptable compared to the base shear reduction rate of frames with LRB-2. In terms of story drift, the performance of the 8 and 12-story frames with the PYSDRB were not suitable to compare with the LRB, but the performance of the 3-story frame was acceptable. Considering low target displacement in bearings design, the PYSDRB performance was better than the LRB in low frame height.