Fibre reinforced plastic (FRP) composites play an important role in lightweight construction due to their high specific stiffness and design flexibility. As a subject of ongoing research, the gradation of fibre distributions and fibre contents is a tool to further improve the efficiency and performance of FRPs. The gradation leads to a locally varying microstructure and thus effective material properties that have to be determined in order to understand and simulate the macromechanical behaviour. The established method for computing the local effective stiffness for an ungraded structure is the utilisation of representative volume elements (RVEs). However, employing this procedure for a graded material requires solving an RVE at every material point of the macro model. This approach, called the FE2 method, remains computationally expensive despite rapid advancements in numerical methods. Therefore, more efficient strategies are required. In the present work, the capabilities of neural networks (NN) are leveraged to predict the effective elastic properties of short fibre reinforced plastics (SFRPs), thus replacing the micro-level RVE calculations. Instead, FE simulations of RVEs, generated from a wide range of input parameters, are used to build a training dataset. The variation of inputs includes the fibre orientation distribution, fibre length, fibre radius, fibre volume content and elastic constants of the constituents. The RVEs are simulated with an FFT-based research FE code, allowing efficient data generation. The resulting NN enables the prediction of the effective stiffness for any arbitrary microstructure and matrix-fibre material combination that may occur in a graded SFRP composite. Once trained, the NN replaces conventional material models on the microstructure level by predicting the effective properties of thousands of material points quasi-instantaneously, resulting in tremendous savings in time and computational cost.