A high-resolution, three-dimensional, primitive-equation model is used to study frontogenesis. The initial state includes a surface front and geostrophic jet. A small initial disturbance grows rapidly into a steepened backward-breaking wave, characterized by narrow wave trough and broad wave crest. Analysis of the energetics indicates that the unstable waves are generated by baroclinic instability. The wavelength scales as the baroclinic deformation radius, but the growth rate appears to be much faster than found in previous primitive-equation model studies. The predicted downward velocity also is an order of magnitude greater than found in previous model studies. As the amplitude of unstable wave becomes very large, a narrow density front whose width is less than the deformation radius, is formed in the wave trough. The frontal zone is marked by high cyclonic vorticity (relative vorticity > f) and intense surface subduction (50–100 m day−1). The frontogenesis is caused by the interaction between synoptic-scale confluence and mesoscale convergence. The strong vertical circulation associated with frontal waves may play a major role in the material exchange and biological production in frontal zone.