The self-organizing feature map is one of the most widely used neural network paradigm based on unsupervised competitive learning. However, the learning algorithm introduced by Kohonen is very slow when the size of the map is large. The slowness is caused by the search for large map in each training steps of the learning. In this paper, a fast learning algorithm based on incremental ordering is proposed. The new learning starts with only a few units evenly distributed on a large topological feature map, and gradually increases the number of units until it covers the entire map. In middle phases of the learning, some units are well-ordered and others are not, while all units are weekly-ordered in Kohonen learning. The ordered units, during the learning, help to accelerate the search speed of the algorithm and accelerate the movements of the remaining unordered units to their topological locations. It is shown by theoretical analysis as well as experimental analysis that the proposed learning algorithm reduces the training time from O (M2) to O (log M) for M by M map without any additional working space, while preserving the ordering properties of the Kohonen learning algorithm.