A new digital predistortion technique based on a direct learning architecture is proposed for linearising power amplifiers (PAs) with nonlinear memory effects. It is based on the non-uniform memory polynomial (MP) model and with a quadratically interpolated LUT. There are mainly two innovations. First, compared with the conventional MP model, the non-uniform MP model achieves the same modelling accuracy with less coefficients. Secondly, compared with the linearly interpolated LUT, the quadratically interpolated LUT has higher accuracy, which is adopted to realise a part of the mathematical computations in the predistortion. The proposed solution is validated on a real PA ZFL-2500. It reduces the number of the model's coefficients and achieves a spectrum regrowth suppression of about 15 dB with a table size of only 8.