The objective of this article is to investigate the pricing problem for the lookback options with American type constrains. Based on the di®erential linear complementary formula associated with the pricing problem, an implicit di®erence scheme is constructed and analyzed. We show that the difference solution is uniquely existent and unconditionally stable. Using the notion of viscosity solutions, we also prove that the finite di®erence solution converges uniformly to the viscosity solution of the continuous problem. Furthermore, by means of the variational inequality analysis method, the O (Δt+h2) order error estimate is derived in the discrete L2-norm provided that the continuous problem is suffciently regular.