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It is usually assumed that different lines of business are independent, but the fact is that they are dependent to some extent in multi-lines of business. Their dependence may be captured by Vine Copula functions. Vine Copula is a powerful tool to solve multiple dependence. Under the assumption that the incremental paid claims of every line of business follows gamma distribution, inverse-Gaussian distribution and log-normal distribution, respectively, the corresponding Vine Copula regression models are established. The model is applied to a real data set of auto insurance and the result shows that the Vine Copula-based regression model is superior to independent regression models in claims reserving. [ABSTRACT FROM AUTHOR]