The pounding of adjacent building is one of the key issues that occurs during earthquakes, which has caused severe damage in buildings. This paper presents an analysis of using an innovative viscous plane damper in the gap between adjacent reinforced concrete (RC) buildings subjected to seismic loads. For this purpose, parallel RC structures of three and six storeys are considered, and a viscous plane damper is implemented in the gap between the two adjacent structures. The effect of the viscos plane damper on the pounding of the considered adjacent RC structure is studied. The finite element modelling and seismic time history analysis of the buildings were performed using Arcs 3D software to prepare the building model. The maximum displacements in horizontal, transverse, and vertical directions are evaluated. Two stages of analysis were conducted. The first stage analysed three-storey and six-storey buildings independently. The results of the first stage were validated with experimental and numerical results. The second stage was analysed by combining two buildings with different storey heights with and without the viscous plane damper. The results showed an effective reduction in displacement values at around 23.15% horizontally, 35.5% transversely, and 14.0% vertically. Therefore, the innovative damper significantly decreased pounding between RC buildings.