The American option pricing problem can be described mathematically bythe well-known Black-Scholes equation with a free boundary. It is difficult to solvethis problem since the free boundary is unknown.To accomplish that, we make use of the Implicit Finite-difference Method and Penalty Method which means to add a continuous penalty term with a small parameter 2 into the Black-Scholes equation,to transform the original free boundary problem into a nonlinear partial differential equation with a fixed boundary.