Land use and land cover change (LUCC) is an important issue in global environmental change and sustainable development, yet spatial simulation of LUCC remains challenging due to the land use system complexity. The cellular automata (CA) model plays a crucial role in simulating LUCC processes due to its powerful spatial computing power; however, the majority of current LUCC CA models are binary-state models that cannot provide more general information about the overall spatial pattern of LUCC. Moreover, the current LUCC CA models rarely consider background artificial irrigation in arid regions. Here, a multiple logistic-regression-based Markov cellular automata (MLRMCA) model and a multiple artificial-neural-network-based Markov cellular automata (MANNMCA) model were developed and applied to simulate complex land use evolutionary processes in an arid region oasis (Zhangye Oasis), constrained by water resources and environmental policy change, during the period 2000–2011. Results indicated that the MANNMCA model was superior to the MLRMCA model in simulated accuracy. Furthermore, combining the artificial neural network with CA more effectively captured the complex relationships between LUCC and a set of spatial driving variables. Although the MLRMCA model also showed some advantages, the MANNMCA model was more appropriate for simulating complex land use dynamics. The two integrated models were reliable, and could reflect the spatial evolution of regional LUCC. These models also have potential implications for land use planning and sustainable development in arid regions.