To explore the double null (DN) divertor configuration and the corresponding plasma current (Ip)operation space for supporting the Mega-ampere plasma current operation in the HL-3 tokamak, the relationship between the safety factor q95 and the equilibrium configuration is determined. Combined with the HL-3 first wall structure and the contours of the upper divertor target plate with three different conceptual designs, the free boundary equilibrium code FEEQS is used to design the DN divertor configuration with variant parameters under Ohmic heating. Considering the engineering requirements, the optimal DN configuration parameters such as plasma current Ip =2.5 MA, the toroidal field BT=2.5 T, elongation к=1.78, triangularity δ=0.65 (for BT=3 T, Ipmax=3 MA) are clarified when q95 is not less than 3. For the need of the closed divertor research, the feasible optimization design of the upper single null configuration is further carried out for Ip =2 MA, BT =2.2 T, к =1.64,δ=0.56. These designs provide references for the upper divertor physical research and the operation of the Mega-ampere plasma current discharge on HL-3 tokamak.