The evaporation of an oscillating droplet has been investigated numerically by using the in-house code FS3D (Free Surface 3D), which is used for direct numerical simulations (DNS) of incompressible multi-phase flows. Validations of the numerical simulations have been shown for two cases. The numerical results have been discussed e.g. for the surface evaporation flux, which depends on location and time. This has been the first time that such DNS calculations have been done for the evaporation of a free-oscillating droplet. It could be shown that the evaporation flux for the unsteady conditions differs strongly from the one predicted with a simplified model assuming quasi-steady conditions, up to 30%. This difference may be caused by the moving interface under unsteady conditions. Thus, it is not possible to describe the problem under investigation with available simple models which use the assumption of quasi-steadiness of the process. •The evaporation of an oscillating droplet is investigated by 3D DNS.•The quasi-steady assumption is released.•The simple model using the quasi-steady assumption is unavailable for our work.•The distribution of evaporation flux is independent of the droplet shape.•The evaporation flux is elevated at the poles and the equator.