The inhomogeneity of turbid medium disrupts the coherent vortex structure of vortex beam and causes the formation of speckle pattern. Here, we propose a new, flexible approach to measure the orbital angular momentum (OAM) of vortex beams through turbid medium by convolutional neural network (CNN). The proposed technique directly recognizes the speckle image and obtains the corresponding OAM mode information. The accuracies exceed 99% and 97% in simulations and experiments respectively. In addition, the relationship between the recognition accuracy and environmental noise level, is present. The results show great potential in fiber communication, biomedical imaging and astronomical application, etc.