The invention discloses a double-plunger submersible diaphragm pump system comprising an upper-stage plunger module and a lower-stage plunger module. The upper-stage plunger module and the lower-stage plunger module are driven by a submersible motor. A submersible motor shaft of the submersible motor rotates to drive an upper-stage plunger and a lower-stage plunger to make reciprocating motion reversely. The reciprocating motion of the upper-stage plunger drives a diaphragm to move up and down, and accordingly positive pressure or negative pressure is generated in a well liquid containing cavity above the diaphragm. Through the switching effect of the positive pressure and the negative pressure in the well liquid containing cavity, external well liquid is imbibed into the well liquid containing cavity and then discharged into an oil pipe, and accordingly the well liquid is hoisted to the ground through the oil pipe. Under the premise that the discharge amount is not changed, hydraulic head parameters of a submersible diaphragm pump can be improved by a large margin, the overall efficiency of the submersible diaphragm pump can be further improved, and accordingly a submersible diaphragm pump can be applied to a low-production oil well. The invention further discloses a relay hoisting method of the double-plunger submersible diaphragm pump system.