We report inelastic x-ray scattering measurements of the temperature dependence of phonon dispersion in the prototypical charge-density-wave (CDW) compound 2H-NbSe2. Surprisingly, acoustic phonons soften to zero frequency and become overdamped over an extended region around the CDW wave vector. This extended phonon collapse is dramatically different from the sharp cusp in the phonon dispersion expected from Fermi surface nesting. Instead, our experiments, combined with ab initio calculations, show that it is the wave vector dependence of the electron-phonon coupling that drives the CDW formation in 2H-NbSe2 and determines its periodicity. This mechanism explains the so far enigmatic behavior of CDW in 2H-NbSe2 and may provide a new approach to other strongly correlated systems where electron-phonon coupling is important.