Considering that the distinctions among static hand gestures are the difference between fingers sticking out, a method of grouping and classifying hand gestures step by step by using the information of the quantity, direction, position and shape of the outstretched fingers was proposed this paper. Firstly, the gesture region was segmented by using the skin color information of the hand, and the gesture direction was normalized by using the direction information of the gesture contour lines. Secondly, the finger was segmented one by one by using convex decomposition in the hand gesture image based on the convex characteristic of the gesture shape. Thirdly, the features of quantity, direction, position and shape of the segmented fingers were extracted. Lastly, a hierarchical decision classifier embedded with deep sparse autoencoders was constructed. The quantity of fingers was used to divide the gesture images into groups first, then the direction, position and shape features of the fingers were used to subdivide and recognize gestures within each group. The experimental results show that the proposed method is robust as lighting, direction and scale changes and significantly superior to the traditional method both in the recognition rate and the recognition stability.