Due to rapid changes on the Earth's surface, it is important to perform land cover change detection (CD) at a fine spatial and fine temporal resolution. However, remote sensing images with both fine spatial and temporal resolutions are commonly not available or, where available, may be expensive to obtain. This paper attempts to achieve fine spatial and temporal resolution land cover CD with a new computer technology based on subpixel mapping (SPM): The fine spatial resolution land cover maps (FRMs) are first predicted through SPM of the coarse spatial but fine temporal resolution images, and then, subpixel resolution CD is performed by comparison of class labels in the SPM results. For the first time, five fast SPM algorithms, including bilinear interpolation, bicubic interpolation, subpixel/pixel spatial attraction model, Kriging, and radial basis function interpolation methods, are proposed for subpixel resolution CD. The auxiliary information from the known FRM on one date is incorporated in SPM of coarse images on other dates to increase the CD accuracy. Based on the five fast SPM algorithms and the availability of the FRM, subpixels for each class are predicted by comparison of the estimated soft class values at the target fine spatial resolution and borrowing information from the FRM. Experiments demonstrate the feasibility of the five SPM algorithms using FRM in subpixel resolution CD. They are fast methods to achieve subpixel resolution CD.