The evaluation of the fitness is computationally very expensive for some optimization problems; therefore a genetic algorithm named FAGA with fitness approximate mechanisms is introduced. In order to effectively control the accuracy and frequency of the fitness approximation, a fitness approximate model based on the concept of fidelity was established. The fitness of a particular individual in the population was obtained as weighted averages of other individuals within a certain area, the size of the area was limited by the fitness sharing radius, the weights of different individuals were determined by the non-dimensional Euclidean distances between individuals and the particular one, and whether to use the real fitness functions or not was decided by the fidelity thresholds. Besides, mechanisms of the loss of fidelity was adopted to reduce the approximate errors from spread and accumulation, and mechanisms of removing redundancy individuals in order to reduce the computing consumption was used at the same time. Three benchmark functions were used to test the convergence and effectiveness of FAGA. The test results show that FAGA achieves satisfactory the optimal solution among the three test functions, and more than 60% of the computation can be reduced at the same time.