A recently developed inverse scattering algorithm [A. J. Devaney and M. Dennison, Inverse Probl., 19, 855 (2003) and M. Dennison and A. J. Devaney, Inverse Probl., 20, 1307 (2004)] is described and applied in a computer simulation study of optical diffraction tomography (ODT). The new algorithm is superior to standard ODT reconstruction algorithms, such as the filtered backpropagation algorithm, in applications employing a limited number of scattering experiments (the so-called limited-view case) and also in cases where multiple scattering occurs between the object being interrogated and the (known) background in which the object is embedded. The new algorithm is compared and contrasted with the filtered backpropagation algorithm in a computer simulation of ODT of weakly inhomogeneous cylindrical objects being interrogated in a limited number of scattering experiments employing incident plane waves. Our study has potential applications in biomedical imaging and tomographic microscopy.