Fibre-reinforced polymer (FRP) composites have been widely used in different engineering sectors due to their excellent physical and mechanical properties. Therefore, fast, convenient and accurate prediction tools for both macroscopic mechanical properties and failure of the composites are highly demanded by industry and interested by academia. In this study, two back-propagation deep neural network (DNN) models are developed. The first model is a regression model for predicting macroscopic transverse mechanical properties of FRP laminae, which is based on a data set generated by Discrete Element Method (DEM) simulations of 2000 Representative Volume Element (RVE) with 200 different sets of fibre volume fractions and fibre radii. The second model, which is a classification model based on the results of 1600 DEM simulations of RVEs with a fixed 45 % fibre volume fraction and 3.3μm fibre radius, is developed for predicting microscopic crack patterns of the FRP laminae. The results show that the two developed DNN models are able to predict both the macroscopic transverse mechanical properties and the microscopic cracks of the RVE accurately.