This paper reports the results of a numerical investigation on the non-linear behaviour and load-carrying capacity of CFRP-strengthened cold-formed steel lipped channel columns - in particular, one studies a total of 16 short and long fixed-ended columns. The fully non-linear numerical analyses are based on shell finite element models, carried out in the code ABAQUS, and adopt an elastic-plastic constitutive law to describe the steel material behaviour. The columns are strengthened with carbon fibre sheets (CFS) glued at different outer surface locations (web, flanges and/or lips) and having fibres oriented either longitudinally or transversally - since the aim of the study is to assess the influence of the CFS on the column structural response, bare steel specimens were also analyzed. The numerical results, which consist of non-linear equilibrium paths (applied load vs. axial shortening) and ultimate strength values (most of them associated with local-plate or distortional failure mechanisms), are subsequently compared with experimental values obtained earlier. Finally, on the basis of both the numerical and experimental results, some relevant conclusions are drawn concerning the CFS location and fibre orientation that are most effective to strengthen lipped channel steel columns exhibiting either local-plate or distortional collapses.