The classical one-way approximation extrapolates the wavefield from the surface. At each depth level, time shifts are applied in the spatial and wavenumber domains. These shifts are function of the local velocity model. Following the same strategy as the beamlet migration, we formulate the split-step Fourier method in the curvelet domain. Curvelets are fairly local in the spatial and wavenumber domains, justifying the use of local velocity values in the one-way strategy. The derivation is validated through an application on 3D zero-offset migration in a heterogeneous model. This work should be understood as a first step towards a better understanding of the wave propagation in a multi-scale and multi-directional perspective. These notions are indeed inherent to curvelets.