The choke-mode accelerating structure is one of the higher-order-mode (HOM) damping structures. It has the advantage of relatively simple fabrication and low surface magnetic field. The high-gradient performance of X-band choke-mode accelerating structures has been studied with six different single-cell prototypes. It was observed that high electric field and small choke dimension caused serious breakdowns in the choke which was the main limitation of the high-gradient performance. The choke-mode accelerating structures reached 130~MV/m by decreasing the electric field and increasing the choke gap. The absence of field emission current flash was proposed to be the sign of breakdowns occurring inside the choke, this was verified by the post-mortem observation. A new quantity was proposed to give the high-gradient performance limit of choke-mode accelerating structures due to RF breakdown.