In this paper, we present a new scenario of the early universe that contains a pre-big bang ekpyrotic phase. By combining this with a ghost condensate, the theory explicitly violates the null energy condition without developing any ghostlike instabilities. Thus the contracting universe goes through a nonsingular bounce and evolves smoothly into the expanding post-big bang phase. The curvature perturbation acquires a scale-invariant spectrum well before the bounce in this scenario. It is sourced by the scale-invariant entropy perturbation engendered by two ekpyrotic scalar fields, a mechanism recently proposed by Lehners et al. Since the background geometry is nonsingular at all times, the curvature perturbation remains nearly constant on superhorizon scales. It emerges from the bounce unscathed and imprints a scale-invariant spectrum of density fluctuations in the matter-radiation fluid at the onset of the hot big bang phase. The ekpyrotic potential can be chosen so that the spectrum has a red tilt, in accordance with the recent data from WMAP. As in the original ekpyrotic scenario, the model predicts a negligible gravity wave signal on all observable scales. As such ‘‘new ekpyrotic cosmology’’ provides a consistent and distinguishable alternative to inflation to account for the origin of the seeds of large-scale structure.