We present dark solitons on stripe phase background in a two-component coupled Bose-Einstein condensate. It is demonstrated that there are many different dark soliton profiles, in contrast to the dark solitons reported before. These different profiles are classified qualitatively to four distinctive cases, according to the differences between stripe spatial period and soliton size, and the fluctuation degree of stripe background. The interactions between these different dark solitons are also investigated. These results further enrich our knowl...