Local binary pattern (LBP) based descriptors have shown effectiveness for texture classification. However, most of them encode the intensity relationships between neighboring pixels and a central pixel into binary forms, thereby failing to capture the complete ordering information among neighbors. Several methods have explored intensity order information for feature description, but they do not address the grayscale-inversion problem. In this paper, we propose an image descriptor called local grouped invariant order pattern (LGIOP) for grayscale-inversion and rotation invariant texture classification. Our LGIOP is a histogram representation which jointly encodes neighboring order information and central pixels. In particular, two new order encoding methods, i.e., intensity order encoding and distance order encoding, are proposed to describe the neighboring relationships. These two order encoding methods are not only complementary but also invariant to grayscale-inversion and rotation changes. Experiments for texture classification demonstrate that the proposed LGIOP descriptor is robust to (linear or nonlinear) grayscale inversion and image rotation.