Abstract: In CT reconstruction, challenge of few-view projections is always the focus and difficulty. At present, the method based on spatial iterative reconstruction is primary solution. However, due to high computational complexity of projection and back projection, spatial iterative reconstruction has some problems, such as time-consuming, great demand for hardware resources and other issues. In this paper, a CT reconstruction algorithm which is named INNG-TV based on extrapolation in frequency is proposed to improve the performance. We first convert data, which is sampled from parallel beam, into frequency-domain by Fourier transform and spline 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 minimum total variation, are introduced to image reconstruction in image space.