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• To solve the forecasting problems of time-lead and nonlinearity in a system, a novel grey multivariable model is proposed. • To reduce the morbidity of the model, the solution of the proposed model is deduced through a derivation method. • The grey prediction evolution algorithm is employed to find the optimal value of parameters. • The validity of the new model was verified by three examples and applied to house price forecasting. Time lags or leads and non-linearity of complex systems are critical to address in accurate scientific prediction. However, few studies have focused on time-lead and nonlinear models with limited information. Therefore, this paper aims to develop a novel grey multivariate model with time-lead operator τ and nonlinear factor r from the perspective of this problem. Next, the solution of the proposed model is deduced through a derivation method to reduce the morbidity of the model. Then, the parameter identification of the model is given on the basis of the least-squares method. The grey prediction evolution algorithm is employed to find the optimal value of parameters τ and r to meet the minimum errors. Finally, house prices of Wuhan, Beijing and Shanghai in China are performed to verify the validity and reliability of the new model. The results demonstrate the model we proposed has satisfactory prediction precision, demonstrating that time-lead and nonlinear factor in the model is reasonable. At the end of the paper, the house prices of these three cities from 2022 to 2028 are also predicted. The average annual growth rate in the three regions is 2.49%, 3.57% and 2.97%, respectively. These results are useful to policy analysis regarding house price correlations. They provide insights for market investors and policy makers. [ABSTRACT FROM AUTHOR]