Urban floods are one of the most devastating natural disasters globally and improved flood prediction is essential for better flood management. Today, high-resolution real-time datasets for flood-related variables are widely available. These data can be used to create data-driven models for improved real-time flood prediction. However, data-driven models have uncertainty stemming from a number of issues: the selection of input data, the optimisation of model architecture, estimation of model parameters, and model output. Addressing these sources of uncertainty will improve flood prediction. In this research, a fuzzy neural network is proposed to predict peak flow in an urban river. The network uses fuzzy numbers to account for the uncertainty in the output and model parameters. An algorithm that uses possibility theory is used to train the network. An adaptation of the automated neural pathway strength feature selection (ANPSFS) method is used to select the input features. A search and optimisation algorithm is used to select the network architecture. Data for the Bow River in Calgary, Canada are used to train and test the network.