We study the stability of a static black hole in two-dimensional string theory. In contrast to a d = 4 real black hole, we found that the tachyonic mode has a potential barrier near the black hole, while the graviton-dilaton has a potential well near the black hole. This potential well induces an exponentially growing mode with time. Finally, it turns out that d = 2 static black hole solution is unstable against external perturbations.