An internal combustion engine control apparatus, comprising: inlet temperature detection means that detects an inlet temperature that is a temperature of an inlet of a purification catalyst disposed in an exhaust path of an internal combustion engine; turbine temperature detection means that detects a turbine temperature that is a temperature on an upstream side of the inlet of the purification catalyst, and that is a temperature of an exhaust turbine of a turbosupercharger disposed in the exhaust path; overlap control means that controls a valve overlap that is a state in which an intake valve and an exhaust valve of the internal combustion engine are open at the same time; inlet high temperature determination means that determines whether or not the inlet temperature is lower than an inlet high temperature reference value; and turbine high temperature determination means that determines whether or not the turbine temperature is higher than a turbine high temperature reference value that is higher than the inlet high temperature reference value; wherein when it is determined that the inlet temperature is lower than the inlet high temperature reference value and it is also determined that the turbine temperature is higher than the turbine high temperature reference value, the overlap control means increases a valve overlap amount to an amount that is greater than a turbine high temperature time reference amount; and, when it is determined that the inlet temperature is higher than the inlet high temperature reference value, a fuel injection amount that is supplied to the internal combustion engine is increased without increasing the valve overlap amount by the overlap control means. inlet temperature detection means that detects an inlet temperature that is a temperature of an inlet of a purification catalyst disposed in an exhaust path of an internal combustion engine; turbine temperature detection means that detects a turbine temperature that is a temperature on an upstream side of the inlet of the purification catalyst, and that is a temperature of an exhaust turbine of a turbosupercharger disposed in the exhaust path; overlap control means that controls a valve overlap that is a state in which an intake valve and an exhaust valve of the internal combustion engine are open at the same time; inlet high temperature determination means that determines whether or not the inlet temperature is lower than an inlet high temperature reference value; and turbine high temperature determination means that determines whether or not the turbine temperature is higher than a turbine high temperature reference value that is higher than the inlet high temperature reference value; wherein when it is determined that the inlet temperature is lower than the inlet high temperature reference value and it is also determined that the turbine temperature is higher than the turbine high temperature reference value, the overlap control means increases a valve overlap amount to an amount that is greater than a turbine high temperature time reference amount; and, when it is determined that the inlet temperature is higher than the inlet high temperature reference value, a fuel injection amount that is supplied to the internal combustion engine is increased without increasing the valve overlap amount by the overlap control means.