The next-nearest-neighbor hopping term t′ determines a magnitude, and, hence, the importance of several phenomena in graphene that include self-doping due to broken bonds and the Klein tunneling, which in the presence of t′, is no longer perfect. Theoretical estimates for t′ vary widely, whereas a few existing measurements by using polarization-resolved magnetospectroscopy have found surprisingly large t′, close to or even exceeding the highest theoretical values. Here, we report dedicated measurements of the density of states in graphene by using high-quality capacitance devices. The density of states exhibits a pronounced electron-hole asymmetry that increases linearly with energy. This behavior yields t′ ≈ −0.3 eV±15%, in agreement with the high end of theory estimates. We discuss the role of electron-electron interactions in determining t′ and overview phenomena, which can be influenced by such a large value of t′.