River bank (RB) erosion is a global issue affecting livelihoods and properties of millions of people. However, it has not received enough attention in the Vietnamese Mekong Delta (VMD), i.e., the world’s third largest delta, compared to salinity intrusion and flooding. There have been several studies examining RB and coastal erosion in the VMD using remotely sensed satellite data, but the applied methodology was not adequately validated. Therefore, we developed a novel SRBED (Spectral RB Erosion Detection) method, in which the M-AMERL (Modified Automated Method for Extracting Rivers and Lakes) is proposed, and a new RB change detection algorithm using Landsat data. The results show that NDWI (Normalized Difference Water Index) and MNDWI (Modified Normalized Difference Water Index) using the M-AMERL algorithm (i.e., NDWIM-AMERL, MNDWIM-AMERL) perform better than other indices. Furthermore, the NDWIM-AMERL; SMA (i.e., NDWIM-AMERL using the SMA (Spectral Mixture Analysis) algorithm) is the best RB extraction method in the VMD. The NDWIM-AMERL; SMA performs better than the MNDWI, NDVI (Normalized Difference Vegetation Index), and WNDWI (Weighted Normalized Difference Water Index) indices by 35–41%, 70% and 30%, respectively. Moreover, the NDVI index is not recommended for assessing RB changes in the delta. Applying the developed SRBED method and RB change detection algorithm, we estimated a net erosion area of the RB of –1.5 km2 from 2008 to 2014 in the Tien River from Tan Chau to My Thuan, with a mean erosion width of –2.64 m and maximum erosion widths exceeding 60 m in places. Our advanced method can be applied in other river deltas having similar characteristics, and the results from our study are helpful in future studies in the VMD.