When air injected into silicone oil contained in a horizontal Hele-Shaw cell, a single air bubble forms and grows showing various interesting phenomena. In this study the effects of the bubble front velocity, air injection velocity at a nozzle, fluid properties and cell depth on the stability of the growing bubble were investigated experimentally. By using the modified capillary number involving the aspect ratio, we obtained the onset conditions of the unstable bubble. Also, the bubble width was analyzed both quantitatively and qualitatively. Before the bubble experiences splitting, the bubble front velocity is almost proportional to the air injection velocity. Therefore the latter velocity may be used in a practical sense.