Structure information is ubiquitous in natural scene images and it plays an important role in scene representation. In this paper, third order structure statistics (TOSS) and fourth order structure statistics (FOSS) are exploited to encode higher order structure information. Afterwards, based on the radial and normal slice of TOSS and FOSS, we propose the high order structure feature: third order structure feature (TOSF) and fourth order structure feature (FOSF). It is well known that scene images are well characterized by particular arrangements of their local structures, we divide the scene image into the non-overlapping sub-regions and compute the proposed higher order structural features among them. Then a scene classification is performed by using SVM classifier with these higher order structure features. The experimental results show that higher order structure statistics can deliver image structure information well and its spatial envelope has strong discriminative ability.