To address the issues of unclear modeling mechanism, inadequate extraction of nonlinear features, and conversion errors in the multivariable time-lag damping accumulated grey model $({\rm TLDAGM} (1,N)) $, this study proposes a multivariate damping accumulated nonlinear time-lag discrete grey model. First, linear and nonlinear correction terms are introduced to enrich the model’s grey information structure, which can not only improve the model’s capability to capture nonlinear characteristics in the data, but also ensure compatibility with the classic${\rm GM }(1,1) $ model. Second, numerical integration is employed to address the modelling error resulting from the original model's treatment of the time-driven term as a grey constant and its imprecise formulation of the derivative term. Third, by adopting the idea of discrete grey modeling, the conversion error arising from the transition between differential and difference equations is effectively reduced. An empirical analysis using the output value data of high-tech enterprises in Shanghai in recent years is conducted, and the model parameters are optimized using the quantum particle swarm optimization. Experimental results demonstrate that the proposed model outperforms the ${\rm TLDAGM} (1,N) $ model and several other multivariable grey models in terms of both fitting and prediction accuracy, and exhibits good stability.