Migration and aging-related dilemmas have limited the opportunities for late-life migrants to rebuild social connections and access support. While research on migrants has drawn increasing attention in HCI, limited attention has been paid to the increasing number of late-life migrants. This paper reports a qualitative study examining the social connections and support of late-life migrants. In particular, drawing on the social convoy model, we pay specific attention to the dynamic changes of late-life migrants' social convoy, the supporting roles each convoy plays, the functions ICT plays in the process, as well as the encountered challenges and expectations of late-life migrants regarding ICT-supported social convoys. Based on these findings, we deeply discuss the role of the social convoy in supporting more targeted social support for late-life migrants, as well as broader migrant communities. Finally, we offer late-life migrant-oriented design considerations.