Content offloading technology based on mobile edge computing can effectively reduce the traffic pressure on the backbone network and improve the end user's experience. A content offloading scheme of greedy strategy was designed for the heterogeneous contact rate between end users and small base stations. Firstly, the content optimal offloading problem was transformed into the content maximum delivery rate problem. Secondly, the maximum delivery rate problem was proved to satisfy the submodularity. On this basis, the greedy algorithm was used to deploy the content. The algorithm was able to guarantee its optimality with the probability (1-1/e). Finally, the impacts of content popularity index and cache size on different offloading schemes were analyzed in detail. The experimental results show that the proposed scheme improves the content delivery rate and reduces the content transmission delay at the same time.