Since the orbital angular momentum entangled state can theoretically constitute an infinite-dimensional quantum entangled state, the research on the quantum non-local correlation testing based on it is of great significance to verify the correctness of the quantum mechanics theory. However, during the experimental preparation of quantum states, the orbital angular momentum entangled state prepared is usually a mixed state due to the influence of environmental noise. Starting, starting from the description of the quantum non-local correlation test logic based on Hardy’s theorem and applicable to the orbital angular momentum mixed state, this paper attempts to test its possibility of the first and second order stepnumbers of the Werner-like orbital angular momentum mixed state quantum Non-local association. Theoretical analysis shows that in the first-order and second-order cases, when the degree of mixing satisfies Tr(ρ2)>0.786 and Tr(ρ2)>0.651 respectively, the orbital angular momentum mixed state can be successfully tested for quantum non-local correlation. In addition, the research results of this article also show that the use of Hardy’s theorem with two ladder can significantly increase the range of successful quantum non-local correlation tests compared with one ladder.