Handoff decision making is one of the most important topics in wireless heterogeneous networks architecture as there are many parameters which have to be considered when triggering handoff and selecting suitable access point. More intelligent approaches which reckon user profiles, application requirements, and network conditions must be improved so that desired performance results for both user and network could be provided. In this paper we introduce a new adaptive vertical handoff decision making algorithm in which fuzzy membership functions are optimized by means of genetic algorithm. Genetic algorithm is an adaptive search technique based on natural selection and genetic rules. In addition to that, it takes places in various scientific applications and can be used to adjust the membership functions in fuzzy systems. The purpose of the study is to adjust the shape of fuzzy membership functions, properly, using genetic algorithm in order to achieve optimum handoff performance. The results show that, compared to the several different algorithms performance of the proposed approach with genetic algorithm is significantly improved for both user and network in terms of number of handoff while the other requirements are still satisfied.