Flood forecasting maps are essential for rapid disaster response and risk management, yet the computational complexity of physically-based simulations hinders their application for efficient high-resolution spatial flood forecasting. To address the problems of high computational cost and long prediction time, this thesis proposes to develop deep learning neural networks based on a flood simulation dataset, and explore their potential use for flood prediction without learning hydrological modelling knowledge from scratch.  A Fully Convolutional Network (FCN), FCN with multiple outputs (Multioutput FCN), UNet, Graph-based model and their Recurrent Neural Network (RNN) variants are trained on a catchment area with twelve rainfall events, and evaluated on two cases of a specific rainfall event both quantitatively and qualitatively. Among them, Convolution-based models (FCN, Multioutput FCN and UNet) are commonly used to solve problems related to spatial data but do not encode the position and orientation of objects, and Graph-based models can capture the structure of the problem but require higher time and space complexity. RNN-based models are effective for modelling time-series data, however, the computation is slow due to its recurrent nature. The results show that Multioutput FCN and the Graph-based model have significant advantages in predicting deep water depths (>50 cm), and the application of recurrent training greatly improves the long-term flood prediction accuracy of the base deep learning models. In addition, the proposed recurrent training FCN model performs the best and can provide flood predictions with high accuracy.