The authors studied on some congruence relations among symmetric multiple zeta functions, called symmetric multiple zeta-star values and multiple zeta-star values. They showed a congruence between symmetric multiple zeta-star values and multiple zeta-star values. They also showed that this congruence together with Aoki and Ohno's relation, the sum formula and the generalized height-one duality for multiple zeta-star values directly lead to those for the symmetric counterparts. The authors also showed that a finite sum of \(L*M (k; t)\), which is a polynomial in \(t\) of order at most \(M\) without a constant term, satisfies an inhomogeneous linear differential equation. They also gave unique solution of the differential equation, which was given by the main theorem.