Abstract Heuristic algorithms strengthen researchers to solve more complex and combinatorial problems in a reasonable time. Markowitz’s Mean-Variance portfolio selection model is one of those aforesaid problems. Actually, Markowitz’s model is a nonlinear (quadratic) programming problem which has been solved by a variety of heuristic and non-heuristic techniques. In this paper a portfolio selection model which is based on Markowitz’s portfolio selection problem including three of the most important limitations is considered. The results can lead Markowitz’s model to a more practical one. Minimum transaction lots, cardinality constraints (both of which have been presented before in other researches) and market (sector) capitalization (which is proposed in this research for the first time as a constraint for Markowitz model), are considered in extended model. No study has ever proposed and solved this expanded model. To solve this mixed-integer nonlinear programming (NP-Hard), a corresponding genetic algorithm (GA) is utilized. Computational study is performed in two main parts; first, verifying and validating proposed GA and second, studying the applicability of presented model using large scale problems.