Traditional seismic data sampling must follow the Nyquist sampling theorem;nevertheless, the field data acquisition can't meet the sampling theorem due to missing traces or exploration cost limits, so we need to reconstruct prestack data to meet the requirements for subsequent processing.A seismic data reconstruction method based on the Projections Onto Convex Sets (POCS) algorithm and a complex-valued curvelet transform (CCT) has been introduced in the paper.Firstly, the Projections Onto Convex Sets (POCS) and complex-valued curvelet transform to characterize the local features of seismic data have been introduced.To tackle the disadvantage of slow convergence in traditional threshold parameter during the reconstruction process, the authors also propose an exponential square root decreased threshold and process 2-D seismic data reconstruction with the hard thresholding, which can reduce iterations and improve reconstruction efficiency.The case study of synthetic seismic data shows that the effect of this method is fairly good.The authors applied this technology in real seismic data and obtained a good result.