The seismic data recovery from data with missing traces plays an important role in the later stage seismic processing.The authors studied the sparse transform (F-K transform and Curvelet transform) and popular compressed sensing theory,and then combined the two methods together to build the seismic data recovery model which is based on sparse transform.The F-K transform changes the seismic data from the t-x (time-space) domain into the f-k (frequency-wavenumber) domain.Because of the favorable directionality and locality and multidimensionality,the curvelet transform can represent the seismic data in a more compressible way.On the basis of the recovery model,the missed seismic data are recovered by the two sparse transforms and the recovery results are compared and analyzed.The recovery results prove that the Curvelet transform recovery can get the better reconstruction effect than the F-K transform.Finally the Marmousi2 model and practical seismic data are processed,and the result shows that the seismic data recovery model is correct and effective.