Abstract: A new effective method for pricing American option under the Black-Scholes model using pseudo inversion matrix is proposed and justified. The bases for a pseudo inversion matrix to price an American Option under the Black-Scholes model depend on the complete understanding of the discretization process and stability principles. For the past years, a lot of researchers have applied pseudo inversion matrix in solving system equations, like reconfigurable control system (RCS), Hermitian differential-algebraic system etc. This paper presents a simple pseudo inversion method for American option valuation under Black-Scholes model, through a drifted financial derivative system, discretized from Black-Scholes financial PDE. An illustrative example is given in concrete setting.