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We have proposed a new algorithm for interpolating irregularly sampled seismic data using shaping regularization. The shaping regularization framework is a very general iterative framework, which can be generalized into different commonly known interpolation techniques, such as the iterative thresholding algorithm, iterative rank reduction, and so on. We derive the IST and POCS in the framework of shaping regularization, which indicates that IST and POCS both can be considered as a special type of shaping regularization with corresponding shaping operation. We also propose a faster version of shaping regularization which uses a linear combination of the current and previous shaping regularized model as the new shaping operator. Both synthetic and field data show pleasant interpolation results using nonlinear shaping regularization and also suggest that the faster version of shaping regularization can improve the convergence rate greatly.