In this paper, we propose a novel bit-stream switching scheme for the multiple bit-rate (MBR) video streaming, in which a Wyner-Ziv coded frame is used to overcome the mismatch between the MBR streams when the switching occurs. With the proposed technique, the MBR streams can be independently encoded without losing any coding efficiency. Similar to distributed video coding, the proposed Wyner-Ziv switching scheme also faces the challenge of rate allocation at the server side. To solve this problem, we propose a new correlation model based on the analysis on the reconstructed frames from the streams with different bit rates. Accordingly, the number of transmitted bits can be on-line calculated based on the correlation model without any feedback from the decoder. With the proposed technique, the actually transmitted Wyner-Ziv bits are only few more than the truly requested bits. However, the delay due to the bit requesting process can be avoided.