In the case of optical computed tomography (OpCT) reconstructions for the field comprising obstacle objects, parts of the projection data are lost; hence, the image reconstruction would be always imprecise with conventional OpCT algorithms if no other preprocessing or interpolation approaches are adopted. To solve the problem of the reconstruction with incomplete data, a Lagrange interpolation reprojection-revising (LIRR) algorithm is proposed. First a Lagrange interpolation polynomial is adopted to preestimate the lost projection data. By comparing to the reprojection of the rough reconstructed image in the iteration, the unbiased Lagrange interpolation estimations are retained; otherwise, the biased estimations are revised, ray by ray, with the weighed superposition of the interpolation and the reprojection data. These steps are repeated until all estimations for lost data are acceptable. Reconstruction results of some known algorithms and the LIRR algorithm for two typical tested images, including a circle round opaque object, were compared. Additionally, an emission spectral tomography experiment was also designed to evaluate the LIRR. The simulation and experiment results show the LIRR makes a great improvement in reconstruction precision over the traditional OpCT algorithms and hence has potential application of OpCT reconstructions with incomplete data.