This paper researches the influence of burner rim configuration on the combustion flame structure and behavior of the laminar-premixed gas, which is composed of air and butane. By systematically varying the premixed gas concentration and velocity, not only the velocity and concentration distribution section of smooth combustion, the critical velocity and concentration range of flash back and blow-off are obtained, but also the section of combustion front tip where vibration and rotation occur, and the section where different polyhedral flame exists are obtained. At the same time, the flame image characteristics are captured under these conditions such as the flame being stable, the vibration of polyhedral flame front tip, the rotation of flame and many ribs, respectively. Furthermore, not to change the mixture concentration and velocity, the transitional change is realized from smooth parabolic cone of the flame front to the polyhedral flame front by moving the ring on the nozzle. These findings will help to reveal the formation mechanism of the polyhedral flames and the mechanism of vibration and rotation in the front tip of polyhedral flame.