One conforming and one non-conforming virtual element Hessian complexes on tetrahedral grids are constructed based on decompositions of polynomial tensor space. Both discrete Hessian complexes start from H2-conforming virtual elements, and end with discontinuous P1 element. The middle H(curl, S) virtual elements are constructed by mixing the hessian of H2-conforming virtual elements and the pulling back of H(div; T)-conforming finite element through operator sym(x\times). The local dimensions of the four spaces in the conforming virtual element Hessian complex are (68, 132, 80, 12), while the non-conforming version is (28, 92, 80, 12). They are applied to discretize the linearized time-independent Einstein-Bianchi system.