Parametric images can help investigate disease mechanisms and vital functions. To estimate parametric images, it is necessary to obtain the tissue time activity curves (tTACs), which express temporal changes of tracer activity in human tissue. In general, the tTACs are calculated from each voxel's value of the time sequential PET images estimated from dynamic PET data. Recently, spatio-temporal PET reconstruction methods have been proposed in order to take into account the temporal correlation within each tTAC. Such spatio-temporal algorithms are generally quite computationally intensive. On the other hand, typical algorithms such as the preconditioned conjugate gradient (PCG) method still does not provide good accuracy in estimation. To overcome these problems, we propose a new spatio-temporal reconstruction method based on the dynamic row-action maximum-likelihood algorithm (DRAMA). As the original algorithm does, the proposed method takes into account the noise propagation, but it achieves much faster convergence. Performance of the method is evaluated with digital phantom simulations and it is shown that the proposed method requires only a few reconstruction processes, thereby remarkably reducing the computational cost required to estimate the tTACs. The results also show that the tTACs and parametric images from the proposed method have better accuracy.