The motion-tracking-enhanced MART (MTE-MART; Novara et al. in Meas Sci Technol 21:035401, 2010) has demonstrated the potential to increase the accuracy of tomographic PIV by the combined use of a short sequence of non-simultaneous recordings. A clear bottleneck of the MTE-MART technique has been its computational cost. For large datasets comprising time-resolved sequences, MTE-MART becomes unaffordable and has been barely applied even for the analysis of densely seeded tomographic PIV datasets. A novel implementation is proposed for tomographic PIV image sequences, which strongly reduces the computational burden of MTE-MART, possibly below that of regular MART. The method is a sequential algorithm that produces a time-marching estimation of the object intensity field based on an enhanced guess, which is built upon the object reconstructed at the previous time instant. As the method becomes effective after a number of snapshots (typically 5–10), the sequential MTE-MART (SMTE) is most suited for time-resolved sequences. The computational cost reduction due to SMTE simply stems from the fewer MART iterations required for each time instant. Moreover, the method yields superior reconstruction quality and higher velocity field measurement precision when compared with both MART and MTE-MART. The working principle is assessed in terms of computational effort, reconstruction quality and velocity field accuracy with both synthetic time-resolved tomographic images of a turbulent boundary layer and two experimental databases documented in the literature. The first is the time-resolved data of flow past an airfoil trailing edge used in the study of Novara and Scarano (Exp Fluids 52:1027–1041, 2012); the second is a swirling jet in a water flow. In both cases, the effective elimination of ghost particles is demonstrated in number and intensity within a short temporal transient of 5–10 frames, depending on the seeding density. The increased value of the velocity space–time correlation coefficient demonstrates the increased velocity field accuracy of SMTE compared with MART.