This study proposes a new representation of discrete Non-linear AutoRegressive with eXogenous inputs (NARX) model by developing its coefficients associated to the input, the output, the crossed product, the exogenous product and the autoregressive product on five independent Laguerre orthonormal bases. The resulting model, entitled NARX-Laguerre, ensures a significant parameter number reduction with respect to the NARX model. However, this reduction is still subject to an optimal choice of the Laguerre poles defining the five Laguerre bases. Therefore, the authors propose to use the genetic algorithm to optimise the NARX-Laguerre poles, based on the minimisation of the normalised mean square error. The performances of the resulting NARX-Laguerre model and the proposed optimisation algorithm are validated by numerical simulations and tested on the benchmark Continuous Stirred Tank Reactor.