A fifth-order computational scheme utilizing spline interpolation has been proposed for convection terms. The physical values discretized on finite grid points are locally interpolated with a quintic spline function as a four times continuously differentiable functions. The derivatives, included in the convection terms described as non-conservative forms, are evaluated by differentiating the quintic spline function, instead of using the difference equations consisting of discretized values, as usually done in higher-order upwind schemes. Thus, the present quintic spline interpolation (QSI) method enables us to deal easily with the non-uniform grids and to treat convection terms in the near-wall regions preserving reasonable accuracy. The QSI method is applied to a onc-dimcnsional pure advection problem_ As a result, while slight phase error is included, it is shown that the numerical accuracy in the QSI method is superior to a fifth-order upwind difference in terms of the preservation of peak values in the initial step-shaped scalar distributions. In addition, two-dimensional flow fields in a cavity are solved with the QSI method. The computational results are in good agreement with the results indicated by Ghia and it is proved that the velocity distributions are predicted with the higher accuracy than the fifth-order upwind difference.