Estimating voltage instability of power systems is important for reduction of large blackouts. This paper proposes to use reachability analysis of hybrid systems for predicting voltage instability of a power system. The reachability analysis is performed by computing backward reachable sets for unsafe sets of hybrid automata. The automata represent continuous voltage dynamics and discrete operations by relay devices. The unsafe sets of hybrid automata are also subsets of state space in which a system voltage shows unacceptable levels such as low or high values. With single machine-load bus (SMLB) system with controlled route switching, we show that voltage instability in the SMLB system can be predicted using the reachability analysis. The obtained result implies that voltage instability leading to large blackouts is possibly detected before its occurrence in power systems.