A method for controlling a reducing agent supply apparatus, the method comprising: pressure-feeding a liquid reducing agent in a storage tank using a pump; injecting the liquid reducing agent into an exhaust passage of an internal combustion engine through a reducing agent injection valve when the internal combustion engine is operating; when the internal combustion engine stops, sucking the liquid reducing agent remaining in a reducing agent supply path back to the storage tank to provide suck-back control; wherein the suck-back control is configured to: when a key switch of the internal combustion engine is turned off at t0, closing the reducing agent injection valve and setting an output of the pump to a predetermined value; starting, at t1, the energization of a passage selector valve so that the liquid reducing agent flows from the reducing agent injection valve to the storage tank; opening, at t2, the reducing agent injection valve; after the elapse of a predetermined time t3, stopping the driving of the pump, stopping, at t4, the energization of a three-way selector valve, and opening to air a first reducing agent passage near the pump; stopping, at t5, the energization of a passage selector valve and closing the reducing agent injection valve to end the suck back control of the liquid reducing agent. pressure-feeding a liquid reducing agent in a storage tank using a pump; injecting the liquid reducing agent into an exhaust passage of an internal combustion engine through a reducing agent injection valve when the internal combustion engine is operating; when the internal combustion engine stops, sucking the liquid reducing agent remaining in a reducing agent supply path back to the storage tank to provide suck-back control; wherein the suck-back control is configured to: when a key switch of the internal combustion engine is turned off at t0, closing the reducing agent injection valve and setting an output of the pump to a predetermined value; starting, at t1, the energization of a passage selector valve so that the liquid reducing agent flows from the reducing agent injection valve to the storage tank; opening, at t2, the reducing agent injection valve; after the elapse of a predetermined time t3, stopping the driving of the pump, stopping, at t4, the energization of a three-way selector valve, and opening to air a first reducing agent passage near the pump; stopping, at t5, the energization of a passage selector valve and closing the reducing agent injection valve to end the suck back control of the liquid reducing agent. when a key switch of the internal combustion engine is turned off at t0, closing the reducing agent injection valve and setting an output of the pump to a predetermined value; starting, at t1, the energization of a passage selector valve so that the liquid reducing agent flows from the reducing agent injection valve to the storage tank; opening, at t2, the reducing agent injection valve; after the elapse of a predetermined time t3, stopping the driving of the pump, stopping, at t4, the energization of a three-way selector valve, and opening to air a first reducing agent passage near the pump; stopping, at t5, the energization of a passage selector valve and closing the reducing agent injection valve to end the suck back control of the liquid reducing agent.