In genetic algorithms(GA), a crossover is performed only at one or two places of a chromosome, and the fixed probabilities of crossover and mutation have been used during the entire generation. A GA with dynamic mutation is known to be superior to GAs with static mutation in performance, but so far no efficient dynamic mutation method has been presented. Accordingly in this paper, a GA is proposed to perform a uniform crossover based on the nucleotide(NU) concept, where DNA and RNA consist of NUs and also a concrete way to vary the probabilities of crossover and mutation dynamically for every generation is proposed. The efficacy of the proposed GA is demonstrated by its application to the unimodal, multimodal and nonlinear control problems, respectively. Simulation results show that in the convergence speed to the optimal value, the proposed GA was superior to existing ones, and the performance of GAs with varying probabilities of the crossover and the mutation improved as compared to GAs with fixed probabilities of the crossover and mutation. And it also shows that the NUs function as the building blocks and so the improvement of the proposed algorithm is supported by the building block hypothesis.