Spatiotemporal fusion aims to improve both the spatial and temporal resolution of remote sensing images, thus facilitating time-series analysis at a fine spatial scale. However, there are several important issues that limit the application of current spatiotemporal fusion methods. First, most spatiotemporal fusion methods are based on pixel-level computation, which neglects the valuable object-level information of the land surface. Moreover, many existing methods cannot accurately retrieve strong temporal changes between the available high-resolution image at base date and the predicted one. This study proposes an Object-Based Spatial Unmixing Model (OBSUM), which incorporates object-based image analysis and spatial unmixing, to overcome the two abovementioned problems. OBSUM consists of one preprocessing step and three fusion steps, i.e., object-level unmixing, object-level residual compensation, and pixel-level residual compensation. OBSUM can be applied using only one fine image at the base date and one coarse image at the prediction date, without the need of a coarse image at the base date. The performance of OBSUM was compared with five representative spatiotemporal fusion methods. The experimental results demonstrated that OBSUM outperformed other methods in terms of both accuracy indices and visual effects over time-series. Furthermore, OBSUM also achieved satisfactory results in two typical remote sensing applications. Therefore, it has great potential to generate accurate and high-resolution time-series observations for supporting various remote sensing applications.