We describe a time-efficient reconstruction scheme with a practical approximate scatter and random correction for dynamic PET imaging on scanners with large data sets such as the High Resolution Research Tomograph (HRRT). This dual (histogram/list-mode) reconstruction scheme makes use of the efficiency advantage of both histogram and list-mode reconstructions (i.e. histogram-mode reconstruction is applied to the dynamic frames with a large number of counts, and list-mode reconstruction is applied to the frames with a low number of counts). The practical scatter and random approximation technique is based on a time averaged scatter and random estimate followed by scaling according to the global numbers of true and random events for each temporal frame. The quantitative accuracy of this dual reconstruction scheme including the scatter and random approximation was examined by comparing the time activity curves (TAC) obtained from the images reconstructed using the conventional histogram-mode algorithm and those obtained from applying the dual reconstruction scheme with the practical approximation. A representative dynamic 11C non-human primate study with 14 temporal frames is presented here, and an excellent agreement between the conventional and the proposed scheme was found, while an overall gain of about 35% in time (which depends on the number of dynamic frames; the more frames with a similar spatial activity distribution there are, the more time we gain) and an over 4 times less storage cost for the scatter and random data sets (sinograms) was achieved in this case.