A fast response $CO_2$ ($fCO_2$) analyzer for real-time measurement of carbon dioxide concentration during transient states of internal combustion engines has been developed. This analyzer uses non-dispersive infrared absorption (NDIR) technique for measuring $CO_2$ concentration and Kalman filter for removing noise components from output signals. The analyzer has good linearity, repeatability and drift with a response time of 11 ms; it is sufficiently fast to detect $CO_2$ concentration during transient states of internal combustion engines. The $fCO_2$ analyzer was used to measure transient $CO_2$ concentration of exhaust gas of the SI engine with a standard gas analyzer, and the signal of the $fCO_2$ analyzer was compared to that of the standard gas analyzer. The two concentrations were well matched during the steady state, and the $fCO_2$ analyzer could measure the variations of $CO_2$ concentration during the transient state.