A trap apparatus of condensate water according to the present invention comprises: a neutralizing part including an inlet through which condensate water is introduced, an internal space for containing a neutralizing agent for neutralizing the introduced condensate water, and a condensate water passage through which the condensate water that was neutralized by the neutralizing agent in the internal space is discharged; a discharge part including a storage space for storing the condensate water which is directly or indirectly introduced through the condensate water passage, an outlet which is open in a circular shape so as to discharge the stored condensate water, and a spherical ball capable of closing the outlet by being seated on the outlet, wherein the ball is spaced from the outlet by buoyancy of the condensate water when the condensate water is contained in the storage space above a critical water level, such that the condensate water can be discharged through the outlet, and the condensate water can be neutralized simultaneously with discharging of only the condensate water without exhaust gas.