The grey dynamic model by convolution integral with the first‐order derivative of the 1‐AGO data and n series related, abbreviated as GDMC(1, n), performs well in modelling and forecasting of a grey system. To improve the modelling accuracy of GDMC(1, n), n interpolation coefficients (taken as unknown parameters) are introduced into the background values of the n variables. The parameters optimization is formulated as a combinatorial optimization problem and is solved collectively using the particle swarm optimization algorithm. The optimized result has been verified by a case study of the economic output of high‐tech industry in China. Comparisons of the obtained modelling results from the optimized GDMC(1, n) model with the traditional one demonstrate that the optimal algorithm is a good alternative for parameters optimization of the GDMC(1, n) model. The modelling results can assist the government in developing future policies regarding high‐tech industry management.