Stably stratified turbulence is investigated with the aim of increasing our limitedunderstanding of the vertical structure of this type of turbulent flow. For strongly stratifiedturbulence there is a theoretical prediction that the energy spectra in the vertical directionof gravity are very steep, possessing the well-known formEh(kv)∝N2k−3v,whereNis theBrunt-Väisälä frequency andkvis the vertical wave number, but supporting evidencefrom experiments and numerical simulations is lacking. We conduct direct numericalsimulation (DNS) with uniform background stratification and forcing at large scales.In order to consider the large anisotropic scales only, the vertical energy spectra aredecomposed into large-scale vertical spectraElarge(kv) and small-scale vertical spectraEsmall(kv) using a horizontal demarcation scale. We find that this approach gives results thatare in close agreement withElarge(kv)∝N2k−3vfor the DNS runs performed. This resultholds approximately over the wave-number rangekbkvkoz,wherekbis the buoyancywave number andkozis the Ozmidov wave number, in agreement with theory. Similarly,large-scale vertical spectra of potential energy are found to beEp,large(kv)∝N2k−3v, over anarrower range of wave numbers. The evidence supports the existence of a scale-by-scale balance between inertia and buoyancy occurring in strongly stratified turbulence at large horizontal scales. Finally, the current results are put in the context of ocean turbulence by making a comparison with measurements of vertical shear spectra made in the ocean interior