We calculate and compare the transition paths from graphite to two types of diamond using the variable cell nudged elastic band method. For the phase transition from graphite to cubic diamond, we analyze in detail how the π bonds transit to the σ bonds in an electronic structure. Meanwhile, a new transition path with a lower energy barrier for the transformation from graphite to hexagonal diamond is discovered. The path has its own peculiar sp-sp bonding configurations, serving as a transition state. Further calculation suggests that the sp-sp transition state represents an expected general phenomenon for cold-compressed graphite.