In X-ray computed tomography (CT), the presence of metal objects in a patient's body produces streak artifacts in the reconstructed images. During the past decades, many different methods were proposed for the reduction or elimination of the streaking artifacts. When scanning a patient, the projection data affected by metal objects (missing projections) appear as regions with high intensities in the sinogram. In spiral fan beam CT, these regions are sinusoid-like curves on sinogram. During the first time, if the metal curves are detected carefully, then, they can be replaced by corresponding unaffected projections using other slices or opposite views; therefore, the CT slices regenerated by the modified sonogram will be imaged with high quality. In this paper, a new method of the segmentation of metal traces in spiral fan-beam CT sinogram is proposed. This method is based on a sinogram curve detection using a curvelet transform followed by 2D Hough transform. The initial enhancement of the sinogram using modified curvelet transform coefficients is performed by suppressing all the coefficients of one band and applying 2D Hough transform to detect more precisely metal curves. To evaluate the performance of the proposed method for the detection of metal curves in a sinogram, precision and recall metrics are calculated. Compared with other methods, the results show that the proposed method is capable of detecting metal curves, with better precision and good recovery.