Under excitations of different periodical signals, the response of a fractional linear system is investigated. First, by the harmonic balance method, the approximate solutions of the fractional-order linear system excited by harmonica signals are obtained. The results in this paper are idenified with the existing results obtained by the average method (Shen Y J, Yang S P, Xing H 2012 Acta Phys. Sin. 61 110505). However, the solving process here is much simpler. Further, the value of the fractional-order is extended in this paper. Then, according to the Fourier expansion and the method of linear superposition, the response of the system to a general periodical signal is obtained, and two examples are given for the case of periodical square wave and modulus of sine wave respectively. The results in this paper show that the value of the factional-order influences the resonance frequency and resonance amplitude of each order harmonic. The monotonicity between the response amplitude and the value of the fractional-order is influenced mainly by the frequency of the external excitation. Besides the analytical analysis, the numerical simulations are also performed, and the approximate solutions are in good agreement with the numerical ones. Hence, the process of the analysis of this paper is feasible.