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In this paper, a genetic algorithm based on Infeasibility Degree (IFD) selection is proposed for constrained optimization problems. Initial solutions and intermediate solutions are allowed to be feasible as well as infeasible as penalty function methods. The infeasibility degree of a solution (IFD) is defined as the sum of the square value of all the constraints violation and the infeasibility degree selection of the population is designed through checking whether the IFD of a solution is less than or equal to a threshold value or not to decide the candidate solution is acceptable or refusable. The method is divided into two stages: first, initial IFD selection is carried out to produce enough initial feasible solution; then the GAs based on Annealing IFD selection is applied to search for the feasible optimum solution. Two selected problems are used to test the algorithm performance.