As a successful case of combining deep learning with photonics, the research on optical machine learning has recently undergone rapid development. Among various optical classification frameworks, diffractive networks have been shown to have unique advantages in all-optical reasoning. As an important property of light, the orbital angular momentum (OAM) of light shows orthogonality and mode-infinity, which can enhance the ability of parallel classification in information processing. However, there have been few all-optical diffractive networks under the OAM mode encoding. Here, we report a strategy of OAM-encoded diffractive deep neural network (OAM-encoded D²NN) that encodes the spatial information of objects into the OAM spectrum of the diffracted light to perform all-optical object classification. We demonstrated three different OAM-encoded D²NNs to realize (1) single detector OAM-encoded D²NN for single task classification, (2) single detector OAM-encoded D²NN for multitask classification, and (3) multidetector OAM-encoded D²NN for repeatable multitask classification. We provide a feasible way to improve the performance of all-optical object classification and open up promising research directions for D²NN by proposing OAM-encoded D²NN.