The droop-based converter plays an important role in a multi-terminal DC (MTDC) system because of its control flexibility. However, this imposes a great challenge on the stability of the DC grid. The main purpose of the paper is to examine the DC side stability of a single grid-connected VSC with the single input single output (SISO) method. The transfer function between the small perturbation of DC-link voltage and DC current at the end of transmission line is first constructed. Based on the SISO model, the stability criteria for a single VSC converter in different control modes is proposed by using the classical Routh judgement. A critical operation index, namely the DC power transfer limit, is defined to assess system stability. Finally, numerical simulation results validate the accuracy of the proposed stability analysis and the criteria for the droop-based converter.This work is supported by the National Natural Science Foundation of China (No. 51807150).