We extend the range of applicability of our previous long-range corrected (LC) hybrid functional, omegaB97X [J.-D. Chai and M. Head-Gordon, J. Chem. Phys. 128, 084106 (2008)], with a nonlocal description of electron correlation, inspired by second-order Moller-Plesset (many-body) perturbation theory. This LC "double-hybrid" density functional, denoted as omegaB97X-2, is fully optimized both at the complete basis set limit (using 2-point extrapolation from calculations using triple and quadruple zeta basis sets), and also separately using the somewhat less expensive 6-311++G(3df,3pd) basis. On independent test calculations (as well as training set results), omegaB97X-2 yields high accuracy for thermochemistry, kinetics, and noncovalent interactions. In addition, owing to its high fraction of exact Hartree-Fock exchange, omegaB97X-2 shows significant improvement for the systems where self-interaction errors are severe, such as symmetric homonuclear radical cations.