Nowadays, the practical applications of shell elements such as beams having thin-wall cross-sections are increasing greatly in various fields of engineering including aerospace, nuclear, marine, and automotive industries. This is due to their ability to optimally use structural materials and simultaneously reduce the total weight of the structure. Fiber polymer composites also have different conspicuous properties such as high stiffness-to-weight and strength-to-weight ratios, corrosion resistance, and high strength. Therefore, laminated composite C-section beam elements simultaneously possess both the beneficial features of fiber-reinforced composite materials and thin-walled cross-sections at the same time. Motivated by these facts, in this research, the flexural-torsional stability of multi-layer fibrous composite tapered beam-columns with channel-section subjected to axial and bending loads is investigated. For this purpose, the total potential energy governing the problem is extracted based on Vlasov’s model for small non-uniform torsion along with the classical laminated plate theory. Then, using Ritz’s methodology as an analytical solution technique, the endurable buckling load is calculated. Eventually, the effect of important parameters such as stacking sequences, fiber composite materials, boundary conditions, axial load eccentricity, and axial preloading on the linear buckling capacity of double-tapered multi-layer composite beam-column with channel-section under axial load and end moment is investigated.