The QUICK scheme for convection terms is modified for unstructured finite volume method by using linear reconstruction technique and validated through the computation of two well defined laminar flows. It uses two upstream grid points and one downstream grid point in approximating the convection terms. The most upstream grid point is generated by considering both the direction of flow and local grid line. Its value is calculated from surrounding grid points by using a linear construction method. Numerical error by the modified QUICK scheme is shown to decrease about 2.5 times faster than first order upwind scheme as grid size decreases. Computations are also carried out to see effects of the skewness and irregularity of grid on numerical solution. All numerical solutions show that the modified QUICK scheme is insensitive to both the skewness and irregularity of grid in terms of the accuracy of solution.