In this paper, we consider a singularly perturbed turning point problem of convection-diffusion of fourth-order ordinary differential equations with a small positive parameter(e). The given fourth-order boundary value problem is transformed into a system of weakly coupled systems of two second-order ordinary differential equations, one without parameter and other with parameter e multiplying highest derivatives with suitable boundary conditions. A computational method is presented for solving the system of both linear and non-linear problems. In the linear case, we first find the zero-order asymptotic approximation expansion of the solution in the second equation. Then, the second equation of the system is solved by the numerical method which is constructed for this problem which involves Shishkin mesh. As in the case of non-linear problem, Newton's method of quasilinearization is applied for the second equation of the system. Numerical results are presented which support the theoretical results. ©Dynamic Publishers, Inc.