The objective of this paper is to study a numerical approximation of a non-local Black-Scholes equation, by means of techniques of discrete mollification and finite differences. We analyze stability of the proposed numerical scheme through monotony and show examples that illustrate its capabilities. Keywords: Black-Scholes, finite differences, discrete mollification. To cite this article: C.D. Acosta, F.C. Osorio, Solucion numerica del modelo Black-Scholes no local por molificacion discreta, Rev. Integr. Temas Mat. 33 (2015), No. 2, 145–160.