The suppression of multiples is a crucial task when processing seismic reflection data. Using the curvelet transform for surface-related multiple prediction is investigated. 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, first it is proposed to decompose the input data into curvelet coefficients. These coefficients are then convolved together to predict the coefficients associated with 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 for exploitation of Snell's law at the sea surface. Moreover, the possible aliasing in the predicted multiple is better managed by using the curvelet multiscale 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 are indeed reduced in the multiple prediction with the use of curvelets, thus allowing for an improved multiple subtraction result.