This First we recall the Giachetti-Johnson (G J) soliton hierarchy based on zero curvature equations from semi-direct sums of Lie algebras.And then we apply the approach, which is based on semi-direct sums of matrix Lie algebras consisting of triangular 4 x 4 block matrix Lie algebras, to construct tri-integrable couplings of the Giachetti-Johnson (G J) hierarchy of soliton equations.Moreover, the Hamiltonian structures of the resulting tri-integrable couplings are worked out by using the variational identity.Finally, we will show that the resulting tri-integrable couplings have a recursion relation Km+l =ΦKm, m≥0.