Numerical simulation has been conducted on a transonic contra-rotating axial compressor to investigate the shock wave and flow characteristics under various operation conditions. Results indicate that the shock-wave structure in the downstream rotor (Rotor 2) of transonic contra-rotating axial compressor is more complex than that in the upstream rotor (Rotor 1). Under the choke condition, a double shock-wave structure appears in the Rotor 2 leading to serious loss. Moving to the design condition, a single shock wave appears at the root and middle sections of blade of Rotor 2, while a normal and an oblique shock wave arise at the blade tip. Under the near-stall condition, the shock structure has no obvious difference from other conditions at the blade root of Rotor 2 but it becomes further off-body at the middle blade. During the switch of transonic contra-rotating axial compressor from the choke to the near-stall condition, the separation bubble on the pressure surface of Rotor 2 decreased gradually due to the increasing aerodynamics load. The suction surface experiences the weakest separation at the design point. Alternatively, the tip leakage flow becomes stronger with maximum loss at the near-stall condition. The radial matching of the meridional passage of Rotor 2 with the routing flow parameters is the potential optimization aspect.