We propose an algorithm, which is based on the wavefnrm relaxation (WR) approach, to coinpnte the periodic sohltions of a linear system described by difierential algebraic equations For this kind of two-point boundary problems, we derive an analytic expression of the spectral set for the periodic WR operator. We show that the periodic WR algorithm is convergent if the snpreinllIn value of the spectral radii for a series of matrices derived froln the system is less than one. Numerlcal examples, where discrete wavefnrms are computed with a backward-difie, rence fnrmnla. filrther ilhlstrate the correctness of the theoretical work in this paper.