Most genetic algorithms do not use the knowledge in the related problem fields completely when searching the approximate solutions. A new kind of genetic algorithm with modified fitness functions the presented in this paper. In this algorithms, both the function value at the searching point and the function change rate at the point are combined into fitness functions. It makes the chromosome code chosen by probability be able to have both smaller function value (for minimum problem) and higher function change rate. The experimental results show that the new algorithm is convergent much faster than the standard genetic algorithm is.