We consider how the 2-D seismic Kirchhoff migration scheme can benefit from a recently introduced shiftable directional pyramid. First, the pyramidal dual-tree directional filter bank is presented with some modifications to make it more suitable to the seismic migration problem. Since the decomposition by this filter bank is multiresolution and multidirectional, it can be regarded as a digital curvelet transform. We implement the first-order approximation of the Kirchhoff migration scheme. It essentially consists of a rotation, a scaling and a shift of each curvelet. These three operations are implemented in the decomposition domain of the filter bank. The reconstructed image using several percentages of highest curvelet coefficients provides a first order approximation of the migrated seismic section. Migration results are presented in the case of homogeneous and non homogeneous background velocity models. We aim at demonstrating that the complex shiftable directional pyramid provides a good quality migrated result.