Petrović in [M. Petrović, On graphs with exactly one eigenvalue less than −1, J. Combin. Theory Ser. B 52 (1991) 102–112] determined all connected graphs with exactly one eigenvalue less than −1 and all minimal graphs with exactly two eigenvalues less than −1. By using these minimal graphs, in this paper, we determine all connected graphs having −1 as an eigenvalue with multiplicity n − 4 or n − 5