Most genetic algorithms now available do not give a convergence rule, and there are difficult problems about premature and slow convergence. To solve these problems, a new kind of genetic algorithms is presented in this paper. Firstly, proceeding from dependent variables of optimized function, a new concept “level set” is introduced.This method can classify population of each generation and arrange all the aim relevant information effectively, so as to obtain the algorithm with high searching speed. Secondly, through the improvement of mutation operator, the diversity of population can be also improved, which avoids the premature convergence effectively. Meanwhile, the new mutation operator is also proved to be able to improve the diversity of population and the new algorithm can converge on the optimum solution. Finally a convergence rule of the algorithm is given. Computer simulations show that its convergence and search speed is faster and its efficiency is higher than other algorithms.