  In this paper, we study the surface energy of the one-dimensional
supersymmetric $t-J$ model with unparallel boundary magnetic fields, which is a
typical $U(1)$-symmetry broken quantum integrable strongly correlated electron
system. It is shown that at the ground state, the contribution of inhomogeneous
term in the Bethe ansatz solution of eigenvalues of transfer matrix satisfies
the finite size scaling law $L^{\beta}$ where $\beta<0$. Based on it, the
physical quantities of the system in the thermodynamic limit are calculated. We
obtain the patterns of Bethe roots and the analytical expressions of density of
states, ground state energy and surface energy. We also find that there exist
the stable boundary bound states if the boundary fields satisfy some
constraints.
