To save the storage and transmission cost, it is applicable now to develop fast and efficient methods to transcode the perennial surveillance videos to HEVC ones, since HEVC has doubled the compression ratio. Considering the long-time static background characteristic of surveillance videos, this paper presents a coding unit (CU) classification based AVC-to-HEVC transcoding method with background modeling. In our method, the background frame modeled from originally decoded frames is firstly transcoded into HEVC stream as long-term reference to enhance the prediction efficiency. Afterwards, a CU classification algorithm which employs decoded motion vectors and the modeled background frame as input is proposed to divide the decoded data into background, foreground and hybrid CUs. Following this, different transcoding strategies of CU partition termination, prediction unit candidate selection and motion estimation simplification are adopted for different CU categories to reduce the complexity. Experimental results show our method can achieve 45% bit saving and 50% complexity reduction against traditional AVC-to-HEVC transcoding.