Recently, various interpolation techniques have been developed for reconstructing the missing traces from the irregularly undersampled seismic data. Among those techniques, a projection onto convex set (POCS) algorithm has gained popularity for its robustness and easy implementation. However, the conventional POCS algorithm using Fourier transform has the limitation in interpolating the seismic data containing curved events. Standard curvelet transform-based POCS algorithm can reconstruct the curved events effectively, but it has trouble in interpolating the weak events when they are interpolated with strong events together. To overcome this problem, we introduce a new curvelet transform-based POCS algorithm which applies curvelet transform to the 2D Fourier transformed data in the frequency-wavenumber domain instead of the data in the time-space domain for each iteration of POCS algorithm. Numerical results clearly demonstrate that the presented algorithm is superior to the standard curvelet transform-based POCS especially for interpolating the data containing various amplitudes.