The sparse scanning imaging methods for x-ray CT is a promising approach to speed up scanning or reduce radiation dose to patients. The major problem for sparse parallel projections is hard to reconstruct high quality image. It suffers severe streak artifacts in reconstruction if the popular filtered back projection (FBP) method is employed. Although several total variation (TV) regularization based algorithms have been developed for sparse-view CT imaging, they still face challenges in both time consumption and computational complexity when the objective image is large. In this paper, a CT reconstruction algorithm, which is named INNG-TV (iterative next-neighbor regridding-total variation), based on extrapolation in frequency is proposed to improve the performance. We first convert data, which is sampled from parallel beam CT, into frequency domain by Fourier transform and linear interpolation. In the following process of iteration, the known data of projection in Fourier space keep constant, whereas the unknown data are estimated by INNG extrapolation. At the same time, prior knowledge and constrained optimization, such as non-negativity constraint and total variation regularization, are introduced to image reconstruction in image space. The numerical simulation results show that the proposed method has better performance in reconstruction quality than ART-TV (algebraic reconstruction technique-total variation). The proposed method not only demonstrates its superiority in time consumption, but also offers outstanding reconstruction quality for sparse-view scan, which makes it significant to sparse-view CT imaging.