A gas concentration measuring apparatus having a gas sensor that is installable in an exhaust system of an internal combustion engine to measure the concentration of the given gas component that is one of oxygen and another gas component contained in exhaust gas emitted from the engine, and being designed to sample an output of the gas sensor which includes a sensor element made of a solid electrolyte body working to produce the output in the form of an electric signal as a function of concentration of a given gas component within a given measurable range, comprising: a heater designed to be supplied with electric power to heat the sensor element; a heater controller working to control a supply of the electric power to said heater to heat the sensor element up to a desired temperature at which the sensor element is activated; and a gas concentration determining circuit designed to sample the output, as produced by the sensor element of the gas sensor, to determine the concentrations of the given gas component, characterized by a sensor element activation determining circuit working to determine a sensor-inputted energy amount (Σ Wh) that is an amount of energy inputted to the sensor element by heat produced by said heater, said sensor element activation determining circuit also working to determine based on the sensor-inputted energy amount whether the sensor element has been placed in an activated state or not of a narrow range defined within the given measurable range, by comparing a first criterion and a second criterion with the sensor-inputted energy amount (Σ Wh), wherein it is determined that the sensor element has been placed in the narrow range activated state when K1 ≦ ΣWh < K2, and it is determined that the sensor element has been placed in the wider range activated state when ΣWh ≧ K2, wherein the sensor element activation determining circuit is configured to, when it is determined that the sensor element has been placed in the narrow range activated state, to determine that the sensor element is so activated as to produce the output as a function of an actual value of the concentration of the given gas component correctly within the narrow range, and when it is determined that the sensor element has been placed in the wider range activated state, to determine that the sensor element is so activated as to produce the output as a function of an actual value of the concentration of the given gas component correctly within a wider range that is the given measurable range, and wherein the sensor element is made of a laminate of the solid electrolyte body and the heater. a heater designed to be supplied with electric power to heat the sensor element; a heater controller working to control a supply of the electric power to said heater to heat the sensor element up to a desired temperature at which the sensor element is activated; and a gas concentration determining circuit designed to sample the output, as produced by the sensor element of the gas sensor, to determine the concentrations of the given gas component, characterized by a sensor element activation determining circuit working to determine a sensor-inputted energy amount (Σ Wh) that is an amount of energy inputted to the sensor element by heat produced by said heater, said sensor element activation determining circuit also working to determine based on the sensor-inputted energy amount whether the sensor element has been placed in an activated state or not of a narrow range defined within the given measurable range, by comparing a first criterion and a second criterion with the sensor-inputted energy amount (Σ Wh), wherein it is determined that the sensor element has been placed in the narrow range activated state when K1 ≦ ΣWh < K2, and it is determined that the sensor element has been placed in the wider range activated state when ΣWh ≧ K2, wherein the sensor element activation determining circuit is configured to, when it is determined that the sensor element has been placed in the narrow range activated state, to determine that the sensor element is so activated as to produce the output as a function of an actual value of the concentration of the given gas component correctly within the narrow range, and when it is determined that the sensor element has been placed in the wider range activated state, to determine that the sensor element is so activated as to produce the output as a function of an actual value of the concentration of the given gas component correctly within a wider range that is the given measurable range, and wherein the sensor element is made of a laminate of the solid electrolyte body and the heater.