Particulate matter emission into the atmosphere is a massive-scale problem. Fossil fuel combustion is an important source of this kind of pollution. The knowledge of total suspended particle (TSP) emissions is the first step for TSP control. The formation of TSP emissions is poorly understood; therefore new approaches for TSP emissions source modelling are required. TSP modelling is a multi-variable non-linear problem that would only require basic information on boiler operation. This work reports the development of a non-linear model for TSP emissions estimation from an industrial boiler based on a one-layer neural network. Expansion polynomial basic functions combined with an orthogonal least-square and model structure selection approach were used for modelling. The model required five independent boiler variables for TSP emissions estimation. Data from the data acquisition system of a 350 MW industrial boiler were used for model development and validation. The results show that polynomial expansion basic functions are an excellent approach to solve modelling problems related to complex non-linear systems in the industry.