Aiming at the problems of low pattern recognition accuracy of high-order composite Laguerre-Gaussian(LG) beams with complex atmospheric turbulence interference and non-zero radial index, a convolutional neural network(CNN) based orbital angular momentum(OAM) pattern recognition method for high-order composite LG beams is proposed. An OAM pattern recognition model based on CNN is constructed to study the influence of different wavelength and transmission distance on the pattern recognition accuracy of radial high-order composite LG beam under complex atmospheric turbulence conditions. The simulation results show that, under the condition of complex atmospheric turbulence, when the transmission distance is 1 km and the CNN training is 100 times, the pattern recognition accuracy of the high-order composite LG beam with wavelength of 850, 1 310 and 1 550 nm is above 98.8%. When the wavelength is 1 550 nm and the transmission distance is 1, 2 and 3 km respectively, the pattern recognition accuracy of the model is above 86.8%.