In this study, a solution for anisotropic conductive heat transfer in a composite cylindrical shell is computed by an exact analytical method. The fibers are considered to be winded around the cylinder at any arbitrary angle. A general linear boundary condition is applied on both circular bases of the cylindrical shell to account for various combinations of thermal conditions. The solution considers the effects of convection of the ambient flow motion and various external radiative heat fluxes. The analytical solution describes the temperature distribution in the axial and circumferential directions. In principle, the heat conduction equation should involve a dual second-order derivation, which precludes solving the equation by the direct application of common exact methods. Therefore, an appropriate canonical mapping is selected as a solution to cancel the dual derivation of temperature in the mapped equations. The separation of variables method is then applied to the mapped equations, which are conducted to obtain an exact form of the solution. Finally, an analytical technique based on the Fourier series concept is proposed to determine unknown coefficients in the final solution. The obtained analytical results correspond well with the solved numerical results. The capability of the current solution is examined by application to a few relevant industrial cases. (C) 2015 Elsevier Ltd. All rights reserved.