In the present paper, a transonic mixed-flow compressor that has relatively lower frontal area than that of centrifugal compressors is discussed, and aerodynamic design as well as performance prediction are performed. Main design constraints are compressor exit Mach number of 0.3 and flow angle of 30degrees at the design point, and maximum overall compressor diameter of 177mm, that is 7.0inch. The mass flow rate of design point and pressure ratio are 1.05kg/s and 5.2:1, respectively. The aerodynamic design results show that the transonic compressor designed with forward-swept inducer and curved diffuser can have the target performance with efficiency of 75% within the given constraints. And the compressor exit flow characteristics are discussed here.