Channels are important geological phenomena in the exploration of oil and gas because they can have a reservoir or destructive nature. In this research, the curvelet transform has been used to improve the quality of the channels in seismic data. For this purpose, by the top-hat morphological operator, the local maxima of the curvelet coefficients in each subband were extracted. In the next step, using the morphological gradient algorithm with the multi-lengths and multi-directions structuring elements, the channel boundaries were extracted. The combination of the curvelet transform with the morphological gradient eliminates many of the false edges generated by the morphological gradient from data. Finally, the proposed method in this study is applied on a real data containing channels and its results were compared with the results of known edge detection algorithms such as Sobel and Laplacian of Gaussian.