Summary: We discuss the ground state and some excited states of the half-filled Hubbard model defined on an open chain with \(L\) sites, where only one of the boundary sites has a different value of chemical potential. We consider the case when the boundary site has a negative chemical potential \(-p\) and the Hubbard coupling \(U\) is positive. By an analytic method we show that when \(p\) is larger than the transfer integral some of the ground-state solutions of the Bethe ansatz equations become complex-valued. It follows that there is a ‘surface phase transition’ at some critical value \(p_c\); when \(p<p_c\) all the charge excitations have the gap for the half-filled band, while there exists a massless charge mode when \(p>p_c\).