The edge structure of graphene has a significant influence on its electronic properties. However, control over the edge structure of graphene domains on insulating substrates is still challenging. Here we demonstrate edge control of graphene domains on hexagonal boron nitride (h-BN) by modifying the ratio of working-gases. Edge directions were determined with the help of both moiré patterns and atomic-resolution images obtained via atomic force microscopy measurements. It is believed that the variation of graphene edges is mainly attributed to different growth rates of armchair and zigzag edges. This work demonstrates a potential approach to fabricate smooth-edge graphene ribbons on h-BN.