Abstract: A second order least squares volume of fluid interface reconstruction algorithm with 81 cells in mesh stencil is introduced.The algorithm is compared with Youngs algorithm and a second order least squares volume of fluid interface reconstruction algorithm with 125 cells in mesh stencil.L^∞ criteria function in three dimensions is used to measure stationary interface reconstruction errors.Stationary and advecting tests show that the algorithm can track any oriented plane exactly and it is second order accurate.Compared with second order least squares volume of fluid interface reconstruction algorithm with 125 cells in mesh stencil,calculation amount of the algoritm is much smaller.Thus CPU time is saved and computing efficiency is improved.