The objective of the study is to investigate the size and shape effect on the efficiency of hybrid Fibre-reinforced polymer (FRP) strengthening of non-circular reinforced concrete (RC) columns under axial compression. FRP strengthening through external bonding (EB) is effective for the confinement of RC columns under axial compression. However, the EB technique is less effective for sections with an aspect ratio (breadth/depth) of more than two. Thus, ACI 440.2R does not consider the beneficial effect of FRP external confinement of columns with an aspect ratio greater than 2.0. Also, the effectiveness of the FRP confinement through EB reduces with the increase in the column size. Though near-surface mounting (NSM) of FRP laminates is less effective under pure axial compression, it can be helpful to meet the increase in strength demands of columns of large size and different shapes. Thus, the hybrid FRP strengthening technique used in this study combines the advantages of EB and NSM techniques. This study focuses on the numerical investigation using a nonlinear finite element analysis software, ABAQUS. Twenty RC non-circular column specimens of 150 mm depth and different size ratios (1.0, 1.5 & 2.0) and aspect ratios (b/d = 1.0, 2.0 & 3.0) are modelled using finite element technique. Different specimens such as (i) control RC with no strengthening, (ii) RC strengthened with EB, (iii) RC with NSM and (iv) RC with hybrid FRP strengthening technique are modelled and studied. The results of the FE analysis are validated using experimental results available in the literature. The validated FE models were used for a detailed parametric investigation to understand the effect of the hybrid combination of NSM ratio (0.4% to 1.6%) for a constant EB ratio. FE results show that hybrid FRP strengthening is effective in strength and ductility improvement of columns with larger size and aspect ratio than other techniques.