Based on compressed sensing (CS), a new multiple description coding method (CS-MDC) was presented. The new method is robust to packet loss or bit error, and has the advantages of simple structure and easy implementation. The method partitioned an image into several blocks by interleaving extracting in the wavelet domain, and made random measurements of the image blocks, and then formed multiple descriptions after quantizing and packing. At the decoding end, it reconstructed the original image approximately or exactly with the received bit streams by solving an optimization problem. The proposed method can construct more descriptions with lower complexity because the process of random measuring is simple and easy to realize. Experimental results show that the proposed method exhibits its superiority over SPIHT-MDC with the same packet loss probability, and it can easily generate more descriptions.