Conformable fractional grey multivariate convolutional (CFGMC($ \alpha, N $)) model introduces the conformable fractional derivative and constant term on the basis of the traditional grey multivariate (GM($1, N $)) model, which not only reflects the influence of the difference of dependent variable information on the data development trend, but also realizes the compatibility with the classical GM($1, 1 $) model. However, the CFGMC($ \alpha, N $) model has some defects, such as single cumulative order of driving factors, simple structure, and conversion error between differential equation and difference equation. Therefore, by setting different conformable fractional accumulation orders to all dependent and independent variables, introducing an additional nonlinear correction term and using the idea of the discrete grey model to eliminate the conversion error, a variable conformable fractional nonlinear discrete grey multivariate model is proposed. Basic properties of the model are analyzed, and the calculation method to compute the optimal accumulation orders is given. Using this model to analyze the corrosion rate of oil and gas pipelines, the results demonstrate that the proposed model exhibits significantly better fitting and prediction accuracy compared to other grey multivariate models, such as the classic GM($1, N $) model and the CFGMC($ \alpha, N $) model.