Aims. Two or more type II bursts are occasionally observed in close time sequence during solar eruptions, which are known as multiple type II bursts. The origin of the successive burst has been interpreted in terms of coronal mass ejections (CMEs) and/or flares. Detailed investigations of the relationship between CMEs and the bursts enable us to understand the nature of the multiple type II bursts. In this study, we examine multiple type II bursts and compare their kinematics with those of a CME occurring near the time of the bursts. Methods. To do this, we selected multiple type II bursts observed by the Culgoora radiospectrographs and a limb CME detected in the low corona field of view (1.4−4 R s ) of a STEREO/SECCHI instrument on December 31, 2007. To determine the 3D kinematics of the CME, we applied the stereoscopic technique to the STEREO/SECCHI data. Results. Our main results are as follows: (1) the multiple type II bursts occurred successively at ten minute intervals and displayed various emission structures and frequency drifting rates; (2) near the time of the bursts, the CME was observed by STEREO and SOHO simultaneously, but no evidence of other CMEs was detected; (3) inspection of the 3D kinematics of the CME using the stereoscopic observation by STEREO/SECCHI revealed that the CME propagated along the eastward radial direction as viewed from the Earth; (4) very close time and height associations were found between the CME nose and the first type II burst, and between CME-streamer interaction and the second type II burst. Conclusions. On the basis of these results, we suggest that a single shock in the leading edge of the CME could be the source of the multiple type II bursts and support the notion that the CME nose and the CME-streamer interaction are the two main mechanisms able to generate the bursts.