We have studied the optical transmission of one-dimensional Fibonacci-class quasiperiodic multilayers, which possess a mirror symmetry. We find that the transmission coefficient is unity for all studied sequences at the central wavelength λ＝λ0, where λ0 ＝ (1/4)nA(B)dA(B) with nA(B) and dA(B) being the index of refraction and thickness of twokinds of layers, respectively. Two-cycle or three-cycle has been found around λ ＝ λ0, which is different from the features of the sequences without symmetric structure.