The invention provides a quick starting system and method for double-tank fused salt heat storage. The quick starting system comprises n oil-salt heat exchangers connected in series, and a salt discharging pipeline and a salt conveying pipeline are arranged between each oil-salt heat exchanger and a salt discharging tank; and a hot fused salt conveying pipeline is arranged between the salt discharging tank and a hot fused salt tank. The quick starting system and method for double-tank fused salt heat storage have the following advantages that by utilizing an original salt discharging system, with the salt discharging tank serving as a container and hot fused salt of the hot fused salt tank serving as a heat source, fused salt circulation between each oil-salt heat exchanger and the salt discharging tank is independently built, the temperature of fused salt in the corresponding oil-salt heat exchangers is increased to the temperature required by an operation working condition, and thus the starting speed of a double-tank fused salt heat storage system can be effectively increased, and the system starting operation flow is simplified. The temperature of the salt discharging tank can be effectively maintained by utilizing heat of fused salt, electric heat tracing energy consumption of the salt discharging system is lowered, and the utilization rate of the salt discharging system at the operation stage is increased.