  The exact solution of the $D^{(1)}_2$ quantum spin chain with generic
non-diagonal boundary reflections is obtained. It is found that the generating
functional of conserved quantities of the system can be factorized as the
product of transfer matrices of two anisotropic $XXZ$ spin chains with open
boundary conditions. By using the factorization identities and the fusion
technique, the eigenvalues and the Bethe ansatz equations of the model are
obtained. The eigenvalues are also parameterized by the zero roots of the
transfer matrix, and the patterns of root distributions are obtained. Based on
them, ground states energy and the surface energies induced by the twisted
boundary magnetic fields in the thermodynamic limit are obtained. These results
are checked by the numerical calculations. The corresponding isotropic limit is
also discussed. The results given in this paper are the foundation to study the
exact physical properties of high rank $D^{(1)}_{n}$ model by using the nested
processes.
