The suppression of multiples is a crucial task when processing seismic reflection data. We investigate how curvelets could be used for surface-related multiple prediction. From a geophysical point of view, a curvelet can be seen as the representation of a local plane wave, and is particularly well suited for seismic data decomposition. For the prediction of multiples in the curvelet domain, we propose to first decompose the input data into curvelet coefficients. These coefficients are then convolved together to predict the coefficients associated to multiples, and the final result is obtained by applying the inverse curvelet transform. The curvelet transform offers two advantages. The directional characteristic of curvelets allows to exploit Snell's law at the sea surface. Moreover, the possible aliasing in the predicted multiples can be better managed by using the curvelet multi-scale property to weight the prediction according to the low-frequency part of the data. 2D synthetic and field data examples show that some artifacts and aliasing effects can be indeed reduced in the multiple prediction with the use of curvelets.