Conventional micro-computed tomography (micro-CT) with high spatial resolution faces the dilemma of a small field of view. In recent years, an electron-beam micro-CT (EBMCT) with a wide field of view has been proposed, which is based on the electron-beam deflection for scanning and multi-microfocus X-ray sources. It can not only maintain the advantage of high spatial resolution, but also greatly expand the field of view of CT scanning and the size of inspectable samples. However, due to the special multi-focus array scanning mode of EBMCT, its projection data encounter both truncation and redundancy. EBMCT generally uses an iterative image reconstruction algorithm that has a low requirement for projection data, but the algorithm requires massive computations and long reconstruction time because the projection data of array focuses are huge, and it is difficult to meet the demand for fast CT scanning and detection by EBMCT. In this paper, a smooth weighted multi-source filtered back-projection (MSFBP) algorithm is proposed. Simulation and experimental results show that the proposed algorithm eliminates artifacts caused by the redundancy of projection data and effectively suppresses truncation artifacts. The quality indicators of reconstructed images, including the root-mean-square error, peak signal-to-noise ratio, structural similarity, and spatial resolution, outperform those of traditional image reconstruction algorithms such as rebinning. Under the same conditions of computer hardware and image matrices, the reconstruction speed of the proposed algorithm is more than 3.3 times faster than that of the simultaneous algebraic reconstruction technique, which lays a good foundation for the application of the EBMCT system in the fast and wide field of view CT detection.