We introduce the hybrid functional HSEsol. It is based on PBEsol, a revised Perdew–Burke–Ernzerhof functional, designed to yield accurate equilibrium properties for solids and their surfaces. We present lattice constants, bulk moduli, atomization energies, heats of formation, and band gaps for extended systems, as well as atomization energies for the molecular G2-1 test set. Compared to HSE, significant improvements are found for lattice constants and atomization energies of solids, but atomization energies of molecules are slightly worse than for HSE. Additionally, we present zero-point anharmonic expansion corrections to the lattice constants and bulk moduli, evaluated from ab initio phonon calculations.