We numerically estimate the maximum Lyapunov exponent of a semiconductor laser with time-delayed optical feed- back using the transient of generalized synchronization. We used an auxiliary system approach to observe generalized synchronization, where a chaotic input signal from a semiconductor laser is injected into two semiconductor lasers with optical feedback and two injected lasers are identically synchronized. The optical injection signal is removed after synchronization, and the two lasers become desynchronized. The maximum Lyapunov exponent can be evaluated by measuring the exponential growth rate of the differences between the outputs of the two desynchronized lasers. The maximum Lyapunov exponent estimated from this method is consistent with that obtained from linear stability analysis. This method can be applied to estimate the maximum Lyapunov exponent in experimental laser systems.