Black-Scholes equation is an important model in option pricing the- ory of flnancial mathematics, and it is very signiflcant in practical applications to study its numerical results. In this paper, we construct a new fully discrete universal difierence scheme of an equivalent initial value problem transformed from Black-Scholes equation via variable-substitutions, and then the schemes of stability proof, the error estimate and the convergence are presented. Fi- nally, the numerical examples of European call options show the e-ciencies and utilities.