In this study, the flame structures of a fuel-rich premixed H2–air mixture issued from a divergent micronozzle were numerically studied and compared with their counterparts. The flame dynamics of the divergent micronozzle at relatively low jet velocities were also analyzed. A flame pattern of “dual flames with a smaller one surrounded by a larger one” was discovered for both the straight and divergent micro-nozzles at high jet velocities. This flame structure began to appear at a lower jet velocity (Vin) as the divergence angle (θ) decreased. Specifically, it first appeared at Vin = 7.5 and 20 m/s for θ = 0° and 5°, respectively. In addition, a flame mode consisting of dual flames with a smaller one inside the nozzle occurred only for divergent micronozzles under low and medium jet velocities. This flame structure could emerge at a higher jet velocity as the divergence angle increased. For example, it could occur until Vin = 5 m/s and 17.5 m/s for θ = 1° and 5°, respectively. A global map of all flame patterns was drawn based on the results obtained by varying the jet velocity and divergence angle. Moreover, periodic flame dynamics appeared when the jet velocity was less than the critical value (<1.7 m/s). Specifically, a small flame (i.e., secondary flame) split from the jet flame (i.e., main flame) and propagated towards the nozzle inlet; however, its propagation direction was inverted and it finally extinguished owing to the heat loss to the nozzle wall. The next cycle was initiated after a short duration. The analysis revealed that the periodic flame dynamics are a result of the thermal interactions between the flame and nozzle wall.