Under the condition that a catalyst temperature Tc of a purification catalyst reaches or exceeds a preset reference temperature Tcref, when a cooling water temperature Tw of an engine is not lower than a preset reference temperature Twref, the internal combustion engine system of the invention sets a target exhaust recirculation rate EGR* based on a given rotation speed Ne of the engine and a given load factor KL and performs exhaust recirculation control to open an EGR valve at a specific angle or opening corresponding to the set target exhaust recirculation rate EGR*. When the cooling water temperature Tw is lower than the preset reference temperature Twref, on the other hand, the internal combustion engine system of the invention sets a fuel increment amount α based on the given rotation speed Ne of the engine and the given load factor KL and performs fuel increment control to increase the specific amount of fuel, which is set relative to the amount of intake air to attain the stoichiometric air-fuel ratio as a value to be injected from a fuel injection valve, by the set fuel increment amount α. This arrangement effectively prevents overheat of the purification catalyst while minimizing the deterioration of fuel consumption.