Genetic Algorithms (GA) are a search techniques based on mechanics of nature selection and have already been successfully applied in many diverse areas. However, increasing samples show that GA's performance is not as good as it was expected to be. Criticism of this algorithm includes the slow speed and premature result during convergence procedure. In order to improve the performance, the population size and individuals' space is emphatically described. The influence of individuals' space and population size on the operators is analyzed. And a novel family genetic algorithm (FGA) is put forward based on this analysis. In this novel algorithm, the optimum solution families closed to quality individuals is constructed, which is exchanged found by a search in the world space. Search will be done in this microspace. The family that can search better genes in a limited period of time would win a new life. At the same time, the best gene of this micro space with the basic population in the world space is exchanged. Finally, the FGA is applied to the function optimization and image matching through several experiments. The results show that the FGA possessed high performance.