Graphene has recently been proposed as an attractive material in saturable absorption (SA) applications due to its broad operation range, low saturation power, easy fabrication, high reliability, and quick recovery time. In this paper, we use laser-induced deposition to prepare graphene saturable absorber, and apply it in a mode-locked all-normal-dispersion (ANDi) Yb-doped fiber laser to experimentally investigate different operational states. By adjusting a polarization controller (PC) and the pump power, bright pulses, dark-bright pulse pairs and their second-harmonic pulses, as well as dark pulses and their second, third-harmonic pulses can all be obeserved. In particular, it is the first time to our knowledge to report on the formation of dark-bright pulse pairs, dark pulses and their harmonic mode locking (HML) counterparts in graphene-based passively mode-locked Yb-doped fiber laser with ANDi cavity. Accoding to simulation, the main causes of these pulses are different cavity nonlinear effects which result from the fiber mode-lock members including graphene. Bright pulses, dark pulses and dark-bright pulse pairs are determined both by the laser structure and their own initial signals. Bright pulse harmonic generation is ascribed to the noise gains which form new components. However, it is found that the multiple-time repetition rate of dark pulses is a result of square pulse splitting of each component. This consequence may be of potential application in new type mode-locked fiber lasers.