A data-driven inverse design method based on neural networks is proposed for turbomachinery. In the devised methodology, design parameters are provided as input to the neural network, and performance attributes, e.g. efficiency, as output. Once trained, the network is used for inverse design, i.e. target performance values are prescribed to generate various design parameter sets. Through empirical experiments, it is observed that the true efficiency of the network-generated radial turbine and thrust bearing designs are in good agreement with the prescribed target efficiencies. Furthermore, the proposed model can be used to accurately generate designs beyond the range of the training data set, showing strong generalization properties. The proposed approach offers the additional benefit of easy implementation, being fully data-driven and not requiring any modifications to the data generation process. As long as data is available, the method can readily be extended to account for multi-component and multi-physics aspects. After a model is trained using a set of design parameters, the proposed method can also be used to generate a subset of design parameters for prescribed target attributes with ease. The data-driven inverse design method represents a novel design approach in the age of big data, and is highly relevant and applicable for turbomachinery designs where an abundance of design data, pairing design parameters and target attributes is available. Notably, through generating a large variety of accurate designs with improved performance, the proposed method effectively indicates trust regions in the design space where further design explorations could be carried out, showing a significant impact on optimisation strategies.