River networks are important water carriers that provide a multitude of ecosystem services, including freshwater for agriculture, drinking water for cities, and recreational activities. Accurate mapping of river networks from remote-sensing images is important for the study of these systems. Unfortunately, the delineation of river networks is challenging due to the meandering nature of river channels, the often complex and variable features of the surrounding landscape, and the spatial heterogeneity of the river networks. Here, we present an adaptive, multi-scale region growth method (AMRGM) to delineate river networks from sentinel-2A/B MSI images. The method can handle variable river heterogeneous surroundings, multiple spatial scales, and variable curvatures of the river channels. The method includes four steps: (1) a water index (NDWI) is used to provide initial detection of river water pixels in the image; (2) a bias-corrected fuzzy C-means (BCFCM) method alleviates the effects of the variable surrounding landscape; (3) a scale-enhancement algorithm based on the hessian matrix makes full use of scale and direction information to enhance river morphology characteristics (multiple dimensions and variable curvatures), and (4) a regional growth criterion facilitates handling of various river dimensions. Fast-growing and fine-screening strategies are also included in the AMRGM. The method is applied to eight river networks to evaluate its accuracy and reliability with various river morphologies and hydrological conditions. The AMRGM is more widely applicable than four commonly used river-detection methods (i.e., K-means method, maximum likelihood method, iterative self-organizing data analysis technique algorithm, and support vector machine) and outperform these methods when detecting multi-scale river branches. The mean overall accuracy (OA) and kappa coefficients (KC) of the AMRGM exceed 97% and 0.92 across the eight river networks. The most accurate river extractions are obtained for large rivers such as the Amazon River, Mackenzie River, and Ganges River Delta, which have more discernable scale and direction characteristics. Relatively high omission and commission errors are observed in river networks with complex and heterogeneous zonations, such as the river Welland, UK, and the Zagya Zangbo River in the Tibet plateau. The complex geomorphic features of the river Welland reduce OA and KC to 93.8% and 0.86, respectively