Hyers-Ulam stability is a basic sense of stability for functional equations. In the present paper we discuss the Hyers-Ulam stability of series-like iterative equations with variable coefficients. By the construction of a uniformly convergent sequence of functions we prove that if we can find a C1 approximate solution of such an equation, then there must be a unique C1 solution of this equation which is close to the C1 approximate solution.