This paper conducts aerodynamic design of a high specific speed mixed flow micro-compressor used as an actuator for Co-flow Jet (CFJ) Active Flow Control (AFC) airfoil. The aerodynamic design poses several challenges, including: 1) Small size with very low Reynolds number; 2) High specific speed for mixed-flow compressor due to high mass flow rate and low total pressure ratio; 3) Static pressure ratio lower than 1 to match the low pressure of CFJ airfoil leading edge (LE) suction peak. The numerical design approach is validated with a mixed flow micro-compressor with very good agreement between the predicted performance and the measured data. Front loaded rotor blade work distribution is adopted to decrease boundary layer loss at the blade surface. Free vortex work distribution is applied for the rotor span to reduce spanwise mixing loss. The rotor efficiency achieved by the numerical prediction is 91.7%. Significant loss is observed downstream of the rotor when the flow reaches the stator and the outlet guide vane (OGV). For the stator, it is found that an inlet and outlet flow path area ratio of 1.05 achieves a very high total pressure recovery of 99.29%. A very good stage isentropic efficiency of 84.3% is achieved. The final design of micro-compressor achieves a flow coefficient of 0.3 at the design point with a total pressure ratio of 1.117 and a static pressure ratio of 0.987. A structure FEM analysis indicates that the rotor blades satisfy the structure strength and modal frequency requirement.