We present optical tomography methods for a 3D refractive index reconstruction of weakly scattering objects using LED light sources. We are able to record holograms by minimizing the optical path difference between the signal and reference beams while separating the scattered field from its twin image. We recorded multiple holograms by illuminating the LEDs sequentially and reconstructed the 3D refractive index reconstruction of the sample. The reconstructions show high signal-to-noise ratio in which the effect of speckle artifacts is highly minimized due to the partially incoherent illumination of the LEDs. Results from combining different illumination wavelengths are also described demonstrating higher acquisition speed.