Optical diffraction tomography (ODT), using an interferometric microscopy technique, can quantitatively measure the three-dimensional (3-D) refractive index (RI) distribution in transparent samples. ODT features unique advantages such as non-invasive, label-free, and high-resolution imaging; these capabilities have been increasingly explored recently, particularly in the field of cell biology. Normally, the RI map is reconstructed by solving the inverse scattering problem using more than one hundred holograms, which correspond to various angles of illumination. Current reconstruction methods all require that each hologram is created by only one illumination angle. Therefore, the number of measurements must be equal to the number of needed illumination angles, thus limiting ODT for video-rate or real-time imaging applications. To overcome this issue, we propose a new ODT system together with a new reconstruction algorithm. In the proposed optical system, the illumination is multiplexed by coding a digital micromirror device to display a series of Lee holograms, each of which corresponds to a plane wave of a specific incident angle in the sample plane. On the other hand, the reconstruction algorithm uses the beam propagation method to model the sample scattering process, as well as the error propagation method to train the artificial neural network which represents the RI distribution of the sample. This novel method is expected to reduce the measurement time by a factor of 4-6, which is crucial for video rate or even real time tomography imaging applications such as label-free 3-D imaging cytometry.