Usage‐based insurance (UBI) provides reasonable vehicle insurance premiums based on vehicle usage and driving behavior. In general, there are three major issues in realizing intelligent UBI systems. First, UBI evaluation mechanisms are not auditable to drivers. Insurers may thus deliberately adjust the UBI premiums. Second, the process of collecting driving data by insurers may lead to serious privacy breaches. Third, forging safer driving data for reducing insurance premiums may cause economic losses for insurers. To address these challenges, in this study, we propose CCUBI, a cross‐chain‐based premium competition scheme with privacy preservation for intelligent UBI systems. We introduce tamper‐resistant blockchain and smart contracts to construct credible insurance mechanisms. The cross‐chain technology connects these blockchains in the entire network to form an open premium competition scheme. Vehicle owners can assess designated insurers by sharing historical data with them to get a suitable CCUBI plan. In addition, we propose a data aggregation method used for CCUBI analysis with privacy preservation. Vehicle owners only publish proofs of the driving data. Proofs can still maintain privacy and computability in cross‐chain flows. Finally, we adopt roadside units to detect forged driving data. We conduct a detailed security analysis. Experimental results also demonstrate the efficiency of CCUBI.