Agriculture is important for economic development in most poverty-stricken areas in China, but cropland use is facing challenges due to rapid industrialization and urbanization, causing serious issues for poverty alleviation and sustainable socioeconomic development. Cropland Use Transition (CUT) is one way to alleviate poverty and develop the economy in poverty-stricken areas. This paper chose 16 typical poverty-stricken counties in Western Hubei province as the case area. A morphology index system was established to evaluate CUT, and geographic information system software was used to analyze the temporal-spatial variations in CUT. Using the Radial Basis Function Neural Network (RBFNN) model, contributions of driving factors of population, economy, and industrial structure to CUT were analyzed. The results show that: (1) cropland use morphology can be divided into functional morphology and spatial morphology; (2) the spatial distribution of CUT was high in the north and low in the south, the temporal variation of CUT from 1995 to 2013 showed fluctuations, and the coefficient of CUT changed from 0.460 to 0.649 with a growth rate of 41%; (3) for the driving factors, population factors most significantly contributed to CUT, followed by industrial structure and economic factors. The results obtained in this study are in line with the findings of previous studies. The RBFNN model is suitable for evaluating the contributions of driving factors, which can solve the deficiency in previous studies caused by ignoring the internal relationship and target orientation of driving factors. This study suggests that poverty-stricken counties should narrow the urban–rural divide, encourage balanced labor and investment flow into cropland by formulating relevant economic policies, motivate farmers’ agricultural engagement, and use science and technology to promote CUT and the growth of the agricultural economy, poverty alleviation, and to coordinate urban–rural development.