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In this talk, I will introduce a general method for obtaining the exact solutions of quantum one-dimensional integrable models without U(1) symmetry.Some closed operator product identities for constructing the functional T-Q relations and the Bethe ansatz equations are derived.It is found that a variety of inhomogeneous T-Q relations obeying the operator product identities can be constructed.As the examples, the quantum spin chains with Mobius like topological boundary condition or with generic external boundary magnetic fields are studied.Numerical results for these systems indicate that any choice of the derived T-Q relations gives the complete set of spectrum of the transfer matrix.