Three-order coma is one of the main aberration types to produce mirror disorders of coaxial threemirror astigmatism (TMA) optical system. The variation characteristics of coma in perturbed coaxial TMA optical system is analyzed using vector aberration theory. The solving method and formula of aberration displacement vectors of secondary mirror and three mirror is proposed, and the coma increment coefficient formula caused by secondary mirror and three mirror of system is deduced. It is proved that the three-order coma produced by decenter of tertiary mirror in X-Y plane can be totally compensated by constant ratio of decenter amount of secondary mirror. The coma-free compensation condition of secondary is proposed, and the coma-free decenter conditions of secondary mirror and tertiary mirror are proposed respectively. Two examples of disordered three mirror in coaxial TMA optical system are used to calculate the coma-free compensation condition. Under the condition of coma-free compensate, the all field of view mean coma increment is only 0.6% and 1.9% before disorder, which shows the validity of the proposed coma-free compensation condition.