Kinetic studies of the carbene polymerization of ethyl diazoacetate (EDA) by palladium (Pd) or rhodium (Rh) catalysts were investigated by real-time Fourier transform infrared (FTIR) spectroscopy. Both (L-prolinate)RhI(1,5-cyclooctadiene) and (L-prolinate)RhI(2,5-norbornadiene) mediated EDA polymerization were proved to be first order reactions, suggesting that the formation of “Rh-carbenoid” is the rate determining step. The activation energy (11.24 kJ mol−1) of the polymerization of “carbenes” generated from EDA with (L-prolinate)RhI(1,5-cyclooctadiene) as the catalyst was calculated from kinetic data via the Arrhenius equation. On the other hand, the polymerizations of EDA catalyzed by three kinds of Pd-catalysts were revealed as zero order reactions, suggesting that the rate determining step involves the formation of an EDA–Pd transition state complex through a coordinated step. Refilling more EDA to the (bis(acetonitrile)dichloropalladium)-mediated carbene polymerization system did not change the reaction order. The rate constant increases gradually with the increase of the dosage of the catalyst and decreases with the cycle-index, which proves the formation of “EDA–Pd transition state complex” and the propagating species with Pd–C bonds at the end of the polymer chain.