We have described a new kind of continued fraction which is referred to as an F1,2-continued fraction. The F1,2-continued fraction arises from a subgraph (denoted as F1,2) of the Farey graph. We have given a geometric interpretation of the partial quotients and formulated an algorithm to find F1,2-continued fraction expansion of a number. We have also studied the analogues of certain properties of regular continued fractions in the context of F1,2-continued fractions. © 2015 Elsevier Inc.