It is easy to construct the geometric invariant of a pair of non-coplanar conics in space. It is the crossratio of the 4 intersection points of the two conics with the common line of the two conic planes. In this paper, the algebraic invariant of a pair of non-coplanar conics is derived from the invariant algebra of a pair of quaternary quadratic forms by using the dual representation of space conics. Then, the relationship between the algebraic invariant and the geometric invariant is established.