The exploration of carbon phases with intact massless Dirac fermions in the presence of defects is critical for practical applications to nanoelectronics. Here, we identify by first-principles calculations that the Dirac cones can exist in graphene with stacking fault (SF) induced periodic line defects. These structures are width (n)-dependent to graphene nanoribbon and are thus termed as (SF)n-graphene. The electronic properties reveal that the semimetallic features with Dirac cones occur in (SF)n-graphene with n = 3m + 1, where m is a positive integer, and then lead to a quasi-one-dimensional conducting channel. Importantly, it is found that the twisted Dirac cone in the (SF)4-graphene is tunable among type-I, type-II, and type-III through a small uniaxial strain. The further stability analysis shows that (SF)n-graphene is thermodynamic stable. Our findings provide an artificial avenue for exploring Dirac Ffermions in carbon-allotropic structures in the presence of defects.