The problems of voltage stability have aroused the interest of researchers in the electrical system around the world. It is important to maintain the system stability, or else it would lead to voltage collapse and consequently complete blackout of the system. In this paper the voltage stability indices, Fast Voltage Stability Index (FVSI); Line stability index LQP and Line stability index Lmn are used to determine the stability of a system. These indices are used to identify the most critical line of the system. Under single line outage condition, effect of placing a TCSC in the system on FVSI; Lpq index and Lmn index has been observed. An IEEE 14 bus system has been considered for simulation purpose with PSAT/ matlab.