This paper presents a simplex algorithm for solving portofolio selection problem with transaction costs. The transaction cost function is assumed to be a V-shaped function of the difference between an existing portofolio and a new one. Under some assumptions on the variance-covariance matrix of returns, we transform the non-differentiable and bi-objective programming problem to a mathematical programming problem which can be efficiently solved by a revised simplex algorithm. This method can be used by mutual funds managers in selecting their portofolios.