A catalyst temperature estimating device that estimates the temperature of an upstream end of a catalyst for purifying exhaust gas of an internal combustion engine in an exhaust gas flow direction by executing a smoothing process for upstream end temperature estimation; the temperature of a downstream end of the catalyst in the exhaust gas flow direction by executing either a downstream end temperature estimation process using the estimated upstream end temperature with a smoothing process for downstream end temperature estimation; and calculates a smoothing coefficient for the estimated downstream end temperature used to smooth the estimated downstream end temperature based on the operation state of the internal combustion engine.