Using a two-layer structure consisting of polyethylene terephthalate (PET) and polydimethylsiloxane (PDMS) to support graphene grown by chemical vapor deposition (CVD), we demonstrate a flexible integrated graphene saturable absorber (SA) on microfiber for passive mode-locked soliton fiber laser. This method can optimize the light-graphene interaction by using evanescent field in the integration structure. Moreover, the fiber laser with the in-line microfiber-to-graphene SA can realize the tunabilities of both the 3dB bandwidth of output optical spectrum and the pulse width of soliton. This tunable mode-locked soliton laser has potential applications in optical communication, optical microscopy, and so on.