The objective of this paper is to determine optimal design parameters of a 3/4 coil-type axial magnetic field (AMF) contact used for 126 kV vacuum interrupter. Using central composite design, finite element calculation and response surface analysis method, axial magnetic field characteristics of the contacts with different design parameters were analyzed systematically. Coil thickness, coil height and slot length were chosen as main design parameters. Axial magnetic flux density at current peak, phase shift time and loop resistance of vacuum interrupter were chosen as three optimization indexes. Besides, a severely erosion region on the contact plate was determined after drawn arc experiment with current of 40 kA rms. The area of the severely erosion region was chosen as another optimization index. Summarizing all calculation results, mathematical models between AMF characteristics and design parameters were established. The effect of design parameters on each optimization index was analyzed. Furthermore, an optimized feasible region of design parameters was determined.