Backpropagation (BP) algorithm is the most popular supervised learning algorithm that is extensively applied in training feed-forward neural networks. Many BP modifications have been proposed to increase the convergence rate of the standard BP algorithm, and Quickprop is one the most popular fast learning algorithms. The convergence rate of Quickprop is very fast; however, it is easily trapped into a local minimum and thus it cannot converge to the global minimum. This paper proposes a new fast learning algorithm modified from Quickprop. By addressing the drawbacks of the Quickprop algorithm, the new algorithm has a systematic approach to improve the convergence rate and the global convergence capability of Quickprop. Our performance investigation shows that the proposed algorithm always converges with a faster learning rate compared with Quickprop. The improvement in the global convergence capability is especially large. In one learning problem (application), the global convergence capability increased from 4% to 100%.