Abstract: A consistent hexahedra1 element method for three-dimensional advective problems is presented in this paper. The flow domain is discretized into arbitrary hexahedral elements. A third-order polynomial based on three-dimensional Cartesian coordinates (x, y, z) is adoped as the element interpolating function to make sure that first derivatives and second and third mixed derivatives of the variable functions over the entire domain are continuous. Results from calculations of two examples show that the consistent hexahedral element method has not only of good numerical stability but also of low damping. It is a significant improvement on the precision of numerical solution for three-dimensional advective problems over the non-consistence linear methods and quasi-consistence tetrahedral element method.