We present a detailed study of the quasiparticle contribution to the low-temperature specific heat of an extreme type-II superconductor at high magnetic fields. Within a T-matrix approximation for the self-energies in the mixed state of a homogeneous superconductor, the electronic specific heat is a linear function of temperature with a linear-T coefficient ␥ s (H) being a nonlinear function of magnetic field H. In the range of magnetic fields Hտ(0.15Ϫ0.2)H c2 where our theory is applicable, the calculated ␥ s (H) closely resembles the experimental data for the borocarbide superconductor YNi 2 B 2 C.