A connected graph of diameter d is said to be almost bipartite if it contains no cycle of length 2£ + 1 for all £ < d. An almost bipartite distance-regular graph r = (X, E) is 2-homogeneous if and only if there are constants ')'1, ... ,'Yd such that [ri-1(u) n r1(x) n r1(y)[ = 'Yi holds for all u E X and for all x, y E ri(u) with 8(x, y) = 2 (i=l, ... ,d).In this paper, almost bipartite 2-homogeneous distance-regular graphs are classified. This determines triangle-free connected graphs affording spin models ( for link invariants) with certain weights.