In this paper, we created a dynamic function training rate for the Back propagation learning algorithm to avoid the local minimum and to speed up training. The Back propagation with dynamic training rate (BPDR) algorithm uses the sigmoid function. The 2-dimensional XOR problem and iris data were used as benchmarks to test the effects of the dynamic training rate formulated in this paper. The results of these experiments demonstrate that the BPDR algorithm is advantageous with regards to both generalization performance and training speed. The stop training or limited error was determined by 1.0e-5.