For the reconstruction of time-domain fluorescence molecular lifetime tomography, conventional methods based on the Laplace or Fourier transform utilize only part of the information from the measurement data, and rely on the selection of transformation factors. To make the best of all the measurement data, a direct reconstruction algorithm is proposed. The fluorescence yield map is first reconstructed with a full-time gate, and then an objective function for the inverse lifetime tomography (instead of the lifetime) is developed so as to avoid dealing with the singularity of the zero points in the lifetime image. Through simulations and physical phantom experiments, the proposed algorithm is demonstrated to have high localization accuracy for fluorescent targets, high quantification accuracy for fluorescence lifetime, and good contrast between different fluorescence targets.