The bullwhip effect widely exists in supply chains and shows its significance for the competitiveness of enterprises in supply chains. In this study, we analyze the bullwhip effect in two parallel supply chains with competing products, each one consisting of a supplier and a retailer. A model is detailed for measuring the bullwhip effect in which the demand of retailers follows a similar vector autoregressive model (VAR-like) process. The results show that the bullwhip effect can be characterized as a quadratic function of the standard deviation ratio. The impact of market competition on the bullwhip effect of the supply chain may have the opposite result, which depends on some parameters, including lead time and market competition in the parallel supply chain. The parameters have asymmetric influence on bullwhip effect. Compared with VAR(1) and AR(1) model, the empirical results show that our VAR(1)-like model is closer to reality. Furthermore, we discuss the conclusion of research and its inspiration for supply chain management.