(1) Background: The preoccupation related to the fall, also called fear of falling (FOF) by some authors is of interest in the fields of geriatrics and gerontology because it is related to the risk of falling and subsequent morbidity of falling. This study seeks to classify the acceleration patterns of the center of mass during walking in subjects with mild and moderate knee osteoarthritis (KOA) for three levels of FOF (mild, moderate, and high). (2) Method: Center-of-mass acceleration patterns were recorded in all three planes of motion for a 30-meter walk test. A convolutional neural network (CNN) was implemented for the classification of acceleration signals based on the different levels of FOF (mild, moderate, and high) for two KOA conditions (mild and moderate). (3) Results: For the three levels of FOF to fall and regardless of the degree of KOA, a precision of 0.71 was obtained. For the classification considering the three levels of FOF and only for the mild KOA condition, a precision of 0.72 was obtained. For the classification considering the three levels of FOF and only the moderate KOA condition, a precision of 0.81 was obtained, the same as in the previous case, and finally for the classification for two levels of FOF, a high vs. moderate precision of 0.78 was obtained. For high vs. low, a precision of 0.77 was obtained, and for the moderate vs. low, a precision of 0.8 was obtained. Finally, when considering both KOA conditions, a 0.74 rating was obtained. (4) Conclusions: The classification model based on deep learning (CNN) allows for the adequate discrimination of the acceleration patterns of the moderate class above the low or high FOF.