Utilizing efficiently and securely hydrogen as clean energy source, it is required not only to analyze the experimental data under a certain condition but also to create the mathematical model for the prediction of flame propagation velocity under various conditions. Thus, it is significant to understand the characteristics of dynamic behavior of hydrogen/air premixed flames and to elucidate the effects of addition of inert gas, i.e. carbon dioxide CO2 and water vapor H2O. We performed the experiments of hydrogen explosion in two types of closed chambers to observe spherically expanding flames using Schlieren photography. Wrinkles on the flame surface were clearly observed in low equivalence ratios. Analyzing the Schlieren images, the flame propagation velocity depending on the flame radius was obtained. Increasing the addition of inert gas, the propagation velocity decreased, especially in the case of CO2 addition. The propagation velocity increased monotonically as the flame radius became larger. The appearance of flame acceleration was found, which was caused by the evolution of wrinkles on the flame surface. Moreover, the Markstein length decreased as the concentration of inert gas became higher, indicating that the addition of inert gas promoted the instability of hydrogen flames. Furthermore, the wrinkling factor, closely related with the increment in propagation velocity, decreased as the inert-gas concentration became higher. The wrinkling factor normalized by the propagation velocity of flat flame increased, on the other hand, under the conditions of high inert-gas concentration, except for near the quenching conditions. This indicated that the addition of CO2 or H2O promoted the unstable motion of hydrogen flames, which could be due to the enhancement of the diffusive-thermal effect. Based on the characteristics of dynamic behavior of hydrogen flames, the parameters used in the mathematical model on propagation velocity including flame acceleration was obtained, and then the flame propagation velocity under various conditions was predicted.