The purpose of this paper is to classify objects contained in images by the object categories. A new object feature in computer vision is introduced, that is fractional histograms of oriented gradients (fHoG). Due to the characteristics of fractional calculus, it is a descriptor that represents not only the object shape information but also the object texture details information. Together with pyramid decomposition, the fHoG features could be used to classify objects with similar shape but in different categories. For fHoG feature is some kind of local features, pyramid decomposition is designed to capture the hiding corresponding information between pixels. The two pyramid, spatial pyramid and Laplace pyramid, are both introduced. The former one is easy to compute while the calculation cost increasing fast as the pyramid level increasing. The latter one could save the calculation cost and get a better classification effect. Both of them could significantly improves the classification performance.