The measurement and visualization of transient three-dimensional (3-D) physical parameters (density and temperature) distribution of complex flow fields are critical technologies for the characteristics studies of flow fields in modern energy engineering. Among the optical computed tomography (OCT) methods, Moiré tomography has the advantages of simple optical path structure, strong anti-interference ability and wide measurement range, which is especially suitable for complex flow field measurement in noisy environments. Acquiring the transient phase information from the moiré projection is of great importance for the dynamic 3-D parameters reconstruction of complex flow fields. In this paper, the dynamic phase retrieve methods including Fourier and spatial phase-shifting in moiré tomographic are studied, respectively. In the Fourier method, an adaptive first-order spectrum extraction algorithm for Fourier transform moiré fringe and a phase calculation method are proposed. Through this, the projection phase can be obtained directly by multiplying the inverse Fourier transform of the positive first-order spectrum of deformed fringe with the inverse Fourier transform of the negative first-order spectrum of reference fringe. In spatial phase-shifting method, a spatial phase-shifting- interferometry-based moiré volume computed tomography (MVCT) method was proposed to extract the radial shearing phase distribution of grid moiré fringe. The measured results for the first-order partial derivative of the phase projection of a propane flame both by Fourier and spatial phase-shifting methods in the experimental moiré computed tomography systems are presented. The research will be valuable for monitoring the combustion state in energy engineering.