We study an interesting and challenging problem, online streaming feature selection, in which the size of the feature set is unknown, and not all features are available for learning while leaving the number of observations constant. In this problem, the candidate features arrive one at a time, and the learner's task is to select a "best so far" set of features from streaming features. Standard feature selection methods cannot perform well in this scenario. Thus, we present a novel framework based on feature relevance. Under this framework, a promising alternative method, Online Streaming Feature Selection (OSFS), is presented to online select strongly relevant and non-redundant features. In addition to OSFS, a faster Fast-OSFS algorithm is proposed to further improve the selection efficiency. Experimental results show that our algorithms achieve more compactness and better accuracy than existing streaming feature selection algorithms on various datasets.