The Cloud Radio Access Network (C-RAN) is regarded as the possible implementation approach of the next-generation mobile networks. C-RAN splits a traditional base station into remote radio heads (RRHs) and the base band unit (BBU). Many BBUs are co-located into a centralized BBU pool. This enables the baseband resources to be managed in a centralized BBU pool and thus improves the efficiency. In this paper, a new bandwidth adaptation (BA) mechanism is designed for the C-RAN with the dual connectivity capability. The dual connectivity allows the bearer to be split so as to access more resources from RRHs simultaneously. The new BA mechanism is developed so as to dynamically allocate the resources to establish a new or a handoff bearer. The new BA mechanism is designed with a new downgrading index, which aims to fairly release the proportional resource from more RRHs and then aggregates the released resource to a new or a handoff bearer. Simulation and analysis results illustrate that the proposed BA mechanism reduces both the handoff bearer dropping and the bearer blocking probabilities.