In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph G into a new graph μ(G), we now call the Mycielskian of G, which has the same clique number as G and whose chromatic number equals χ(G)+1. Let μⁿ(G)=μ(μⁿ⁻¹(G)) for n2. This paper investigates the circular chromatic numbers of Mycielski's graphs. In particular, the following results are proved in this paper: (1)  for any graph G of chromatic number ; (2)  if a graph G satisfies with d=2 or 3, then ; (3)  for any graph G of chromatic number 3, χ_c(μ(G))=χ(μ(G))=4; (4) χ_c(μ(K_n))=χ(μ(K_n))=n+1 for n3 and χ_c(μ²(K_n))=χ(μ²(K_n))=n+2 for n4.