A nonlocal harmonic elastic rod model is proposed to describe the elastic behavior of short DNA molecules. We show that the nonlocal interactions contribute to effective bending energy of the molecule and affect its apparent persistence length. It is also shown that the anomalous behavior which has been observed in all-atom molecular dynamic simulations [A. K. Mazur, Biophys. J. 134, 4507 (2006)] can be a consequence of both nonlocal interactions between DNA base pairs and the intrinsic curvature of DNA.