In this paper, we propose a tomographic algorithm for reconstruction of the energy profile of an optical beam from the data measured with a linear bolometer. This algorithm is based on a discrete Fourier transform (DFT). When reconstructing the DFT values and making linear interpolation, we used a raster in the form of concentric squares that essentially decrease the error of reconstruction and save a computation time. In a computer experiment, we have estimated the accuracy of the reconstruction method and determined the optimal number of projections. The proposed algorithm has been successfully used for reconstruction of the beam intensity distribution from the experimental data. The results of reconstruction were compared with the data of direct measurements. It is shown that the proposed algorithm allows most fast reconstruction of spatial energy structure of an optical pulse to be done. The accuracy of reconstruction is not worse than that of the existing algorithms when the noise level is no more than 20%.