To investigate the local micro-/nanoscale region in a large scale sample, an image reconstruction method for nanometer computed tomography (nano-CT) was proposed in this paper. In the algorithm, wavelets were used to localize the filtered-backprojection (FBP) algorithm because of its space-frequency localization property. After the implementation of the algorithm, two simulation local reconstruction experiments were performed to confirm its effectiveness. Three evaluation criteria were used in the experiments to judge the quality of the reconstructed images. The experimental results showed that the algorithm proposed in this paper performed best because (1) the quality of its results had improved 20%-30% compared to the results of FBP and 10%-30% compared to the results of another wavelet algorithm; (2) the new algorithm was stable under different circumstances. Besides, an actual reconstruction experiment was performed using real projection data that had been collected in a CT experiment. Two-dimensional (2D) and three-dimensional (3D) images of the sample were reconstructed. The microstructure of the sample could be clearly observed in the reconstructed images. Since much attention has been directed towards the nano-CT technique to investigate the microstructure of materials, this new wavelet-based local tomography algorithm could be considered as a meaningful effort.