The characteristics of the construction of one-dimensional Fibonacci-class quasilattices (1D FC(n)) have been described.By means of the electric field theory and the properties of unimodular matrix,we studied extensively the transmissive properties of light through multilayers constructed following 1D FC(n) sequence and found that the transmission coefficient for FC(2m) is switch-like(on-off-on-off-…) and there exist six circulative properties for the one of FC(2m+1) around δ=π(1/2±k), in which the number of transmission coefficient shows interesting properties.