Abstract: This paper studies Hamilton properties of the third-order circuit graphs of uniform matroids U_m，n in some conditions. It is proved that when m + 2 ≤ n ≤ 2m - 1，the third-order circuit graphs of U_m，n are Hamiltonian-connected and uniformly Hamiltonian；when n = 2m，the third-order circuit graphs of U_m，2m is Hamiltonian-connected，where m,n ∈ Z^{+，m ≥ 3.}

Key words: uniform matroids, circuit graphs of matroid, Hamiltonian-connected, uniformly Hamiltonian