Static Synchronous Compensator (STATCOM) has been utilized to improve the dynamic behaviors of Line Commutated-Converter based High Voltage Direct Current (LCC-HVDC) system under weak AC grid conditions. However, the close coupling between STATCOM and LCC system could result in system instability especially under weak AC grid conditions, which has not been addressed in the existing literatures. This paper developed a linearized small-signal dynamic model of a LCC system with STATCOM at the inverter busbar, and validated its accuracy by comparing time-domain responses from small-signal model and simulation results from PSCAD/EMTDC. Based on the small-signal model, this paper investigated the impact of STATCOM on the small-signal stability margin of LCC-HVDC by eigen-analysis and participation factor methods. The results show that under weak AC grid conditions, the close interaction between the control system of STATCOM (especially the AC voltage controller) and PLL of LCC system, deteriorates the system stability and may cause oscillation/instability. Then, this paper proposed a novel supplementary coordinated damping-control (SCDC), for LCC-HVDC system with STATCOM under weak AC grid conditions. The results based on the eigen-analysis and electromagnetic transient (EMT) simulations indicate that the proposed SCDC approach can effectively mitigate the oscillations/instability induced by the controller interaction of STATCOM and LCC system, thus effectively improve the stability margin of the overall system.