Projection incompleteness in x-ray computed tomography (CT) often relates to sparse sampling or detector gaps and leads to degraded reconstructions with severe streak and ring artifacts. To suppress these artifacts, this study develops a new sinogram inpainting strategy based on sinusoid-like curve decomposition and eigenvector-guided interpolation, where each missing sinogram point is considered located within a group of sinusoid-like curves and estimated from eigenvector-guided interpolation to preserve the sinogram texture continuity. The proposed approach is evaluated on real two-dimensional fan-beam CT data, for which the projection incompleteness, due to sparse sampling and symmetric detector gaps, is simulated. A Compute Unified Device Architecture (CUDA)-based parallelization is applied on the operations of sinusoid fittings and interpolations to accelerate the algorithm. A comparative study is then conducted to evaluate the proposed approach with two other inpainting methods and with a compressed sensing iterative reconstruction. Qualitative and quantitative performances demonstrate that the proposed approach can lead to efficient artifact suppression and less structure blurring.