We present conservatively remapping cell-centered variables from one mesh to another with second-order accuracy and boundary-preservation. It is generally applicable to any polyhedral source or target mesh. The algorithm consists of four parts:A least square based polynomial reconstruction of physical gradient; an octree-based fast donor-cell searing algorithm; a convex hull algorithm for intersection of polyhedrons and a modifying procedure for local bound preservation. The remapping scheme is scalable, second-order accurate and enjoys bound preservation property. Various benchmark problems demonstrate these properties. Numerical results show that it takes hundreds seconds to remap physical variables on tessellation with hundreds thousands to millions polyhedrons.