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Kumasi is a nodal city and functions as the administrative and economic capital of the Ashanti region in Ghana. Rapid urbanization has been experienced inducing the transformation of various Land Use Land Cover (LULC) types into urban/built-up areas in Kumasi. This paper aims at tracking spatio-temporal LULC changes utilizing Landsat imagery from 1986, 2013 and 2015 of Kumasi. The unique contribution of this research is its focus on urban expansion analysis and the utilization of Random Forest (RF) Classifier for satellite image classification. Change detection, urban land modelling and urban expansion in the sub-metropolitan zones, buffers, density decay curve and correlation analysis were methodologies adopted for our study. The classifier yielded better accuracy compared to earlier works in Ghana. The evaluation of LULC changes indicated that urban/built-up areas are continually increasing at the expense of agricultural and forestlands. The urban/built-up areas occupied 4622.49 hectares (ha) (23.78%), 13,447.50 ha (69.18%) and 14,004.60 ha (72.05%) in 1986, 2013 and 2015, respectively of the 19,438 ha area of Kumasi. Projection indicated that urban/built-up areas will occupy 15,490 ha (79.70%) in 2025. The urban expansion was statistically significant. The results revealed the importance of spatial modeling for environmental management and city planning.