A novel genetic algorithm,simply written as REGA, is proposed with the idea to limit the number of repeating crossover and replacing the worst individuals of the current generation by the best ones of the former generation. The algorithm overcomes the premature phenomenon of the simple genetic algorithm. According to Markov's limitation theorem, we prove its global convergence,explore the properties of the genetic algorithm written as RSGA only based on repeating crossover,and provide a method to calculate the mathematic expectation on the absorption time for the two algorithms. Finally,the simulation shows that the algorithm REGA can solve the optimization problem containing more than one global optimal solutions,on one hand,while eliminating the drawback of local optimum and rapidly enhancing the average fitness. On the other hand, REGA is valuable for function optimization.