Cellular automata (CA) are one of the most common methods for microstructure simulation of metallic materials and are known to offer a reasonable tradeoff between computational cost and physical accuracy, especially if compared with Kinetics Monte Carlo and phase-field simulation strategies. In this study, we develop a neural-networks-based cellular automata framework (NCA) which uses a deep neural network to replace the simple and pre-set updating rules of the traditional CA method.  A discussion on the physical accuracy, computational efficiency, and advantages of the proposed framework is given.  Notably, the flexibility of the NCA simulation strategy allows to better capture details of physical phenomena governing the formation of solidification microstructure when compared with the traditional CA and enables its application for microstructure modeling of complex alloy systems manufactured through advanced processes such as metal additive manufacturing.