Abstract: The study of de-multiple methods is a very important in seismic data processing. With increasing difficulties of oil exploration and the enhancement of seismic imaging accuracy, the existence of multiples seriously degrades the signal to noise ratio of seismic data, and interferes the identification of primary waves. Meanwhile, it may also cause some false geological features in seismic sections. Therefore, how to effectively suppress multiple is always a focused topic in seismic exploration.The current multiple suppression methods can be classified into two categories: based on filtering methods and based on prediction-and-subtraction methods. When using wave equation and considering the properties of wave-field propagation, the prediction-and-subtraction methods are suitable for complex seismic data. However, standard matching or subtraction methods can only correct the amplitude or phase errors between the multiple model and actual multiples in the stage of subtraction. As for the misalignment errors, these methods cannot achieve better results. So, a new curvelet transform named complex curvelet transform (CCT) is proposed. Taking advantage of shift invariance property of CCT, we can use the phase and amplitude of the data's and multiple model's CCT coefficients to correct misalignment and amplitude errors between the multiple model and actual multiples. In addition, for the purpose of protecting primary waves further, a non-linear masking filter is applied in advance, which can separate most of primary waves firstly, then recover the remaining primary waves using the CCT-based separation method.To demonstrate the validity of the CCT-based separation method, the shot gathers of a concave model are simulated. Firstly, the non-linear masking filter is applied to separate the primary and multiple with partial primary. After doing a simple L2 norm matching to the multiple, the CCT-based separation method is adopted to obtain the residual primary. Combining the residual primary and the primary separated by the non-linear masking filter, the final de-multiple data is obtained. Comparing to the standard matching methods, such as the pseudo multi-channel matching method, the CCT-based separation method can directly correct the amplitude and phase of the multiple model, and protect the primary greatly while suppressing the multiple.The test on the field data also shows the proposed method is applicable and effective. The tests on synthetic and field data show that in the case of misalignment error existence, taking advantage of the properties of shift invariance and amplitude changing with coefficient of CCT, the phase and amplitude of the multiple model can be corrected directly to fit the actual multiple. The application of a non-linear masking filter can protect the primary better while suppressing the multiple. And the new method is proved to be applicable and effective.