In this work, two kinds of partial least squares modelling methods are applied to predict a compressor map: one uses a Power function polynomial as the basis function (PLSO), and the other uses a trigonometric function polynomial (PLSN). To demonstrate the potential capabilities of PLSO and PLSN for a typical interpolated prediction and extrapolated prediction, they are compared with two other classical data-driven modelling methods, namely, the look-up table and artificial neural network. PLSO and PLSN are also compared to each other. The results show that PLSO and PLSN have a better prediction performance than the look-up table and the artificial neural network, especially for the extrapolated prediction. At the same time, the computational time is also decreased sharply. Compared with PLSO, PLSN is characterized with higher prediction accuracy and shorter computational time than PLSO. It can be expected that PLSN can be time-saving and improve the accuracy of a thermodynamic model of a diesel engine.