Edge contacts to graphene can offer excellent contact properties. Role of different chemical terminations is examined by using ab initio density functional theory and quantum transport simulations. It is found that edge termination by group VI elements O and S offers considerably lower contact resistance compared to H and group VII element F. The results can be understood by significantly larger binding energy and shorter binding distance between the metal contact and these group VI elements, which results in considerably lower interface potential barrier and larger transmission. The qualitative conclusion applies to a variety of contact metal materials.