We introduce the hybrid broken-ray tomography (HBRT) for three-dimensional imaging of weakly scattering systems. The HBRT utilizes fluorescent contrast agents and combines the principles and advantages of the broken-ray tomography and the non-reciprocal broken-ray tomography introduced by us previously. The HBRT uses angularly resolved intensity measurements at the incident and fluorescence wavelengths to reconstruct the attenuation and scattering coefficients at the excitation wavelength anywhere within the sample, as well as the attenuation coefficient at the fluorescence wavelength and the contrast agent concentration in the regions of contrast agent accumulation. The principles of HBRT have been validated by Monte Carlo simulations.