A control system for an internal combustion engine comprising: an exhaust gas purification apparatus arranged in an exhaust passage of the internal combustion engine and including an NO x catalyst having an ability of reducing NO x and a particulate filter; temperature obtaining means for obtaining the temperature of said NO x catalyst; intake air quantity restriction means that restricts the intake air quantity of the internal combustion engine in such a way as to make it smaller when the temperature obtained by said temperature obtaining means is low than when the temperature obtained by said temperature obtaining means is high; fuel restriction means for restricting a fuel injection quantity in relation to the intake air quantity of the internal combustion engine; trapped PM amount obtaining means for obtaining a trapped PM amount, which is defined to be the amount of particulate matter trapped in said particulate filter; and correction means that corrects a restriction value of the fuel injection quantity, when the trapped PM amount obtained by said trapped PM amount obtaining means is not larger than a predetermined amount and the internal combustion engine is in an accelerating operation state, in such a way that the restriction by said fuel restriction means is more relaxed when the temperature obtained by said temperature obtaining means is low and the intake air quantity restricted by said intake air quantity restriction means is large than when the temperature obtained by said temperature obtaining means is high and/or the intake air quantity restricted by said intake air quantity restriction means is small. an exhaust gas purification apparatus arranged in an exhaust passage of the internal combustion engine and including an NO x catalyst having an ability of reducing NO x and a particulate filter; temperature obtaining means for obtaining the temperature of said NO x catalyst; intake air quantity restriction means that restricts the intake air quantity of the internal combustion engine in such a way as to make it smaller when the temperature obtained by said temperature obtaining means is low than when the temperature obtained by said temperature obtaining means is high; fuel restriction means for restricting a fuel injection quantity in relation to the intake air quantity of the internal combustion engine; trapped PM amount obtaining means for obtaining a trapped PM amount, which is defined to be the amount of particulate matter trapped in said particulate filter; and correction means that corrects a restriction value of the fuel injection quantity, when the trapped PM amount obtained by said trapped PM amount obtaining means is not larger than a predetermined amount and the internal combustion engine is in an accelerating operation state, in such a way that the restriction by said fuel restriction means is more relaxed when the temperature obtained by said temperature obtaining means is low and the intake air quantity restricted by said intake air quantity restriction means is large than when the temperature obtained by said temperature obtaining means is high and/or the intake air quantity restricted by said intake air quantity restriction means is small.