Spatiotemporal fusion (STF) can provide dense satellite image series with high spatial resolution. However, most spatiotemporal fusion approaches are time-consuming, which seriously limits their applicability in large-scale areas. To address this problem, some efforts have been paid for accelerating STF approaches with help of graphics processing units (GPUs), whose effect is dramatic. However, this strategy is hardware dependent, which may not be always satisfied. In this paper, we develop a hardware independent accelerating strategy, named AcSTF. The proposed AcSTF consists of two steps, which are medium resolution STF (MSTF) and local normalization-based fast fusion (LNFM). The MSTF utilizes STF methods to improve the coarse spatial resolution images to a medium spatial resolution, while the LNFM further refines the medium spatial resolution images to provide fine spatial resolution images. To test the AcSTF, the experiments are conducted using five commonly used STF approaches on two public Landsat-MODIS datasets. The experimental results indicate that AcSTF can not only reduce 87%–95% running time of current STF approaches, but also preserve their qualitative and quantitative performance well. After that, we apply the AcSTF to produce an intact 30 m image of the whole Ukraine mainland. Without any hardware which can speed up computing,the time for reconstructing the 30 m image is 5.42 h just using an unremarkable central processing unit (CPU). Compared to the real Landsat image, the reconstructed image achieves remarkable qualitative and quantitative performance, which demonstrates the practicability of the AcSTF.