Cognitive impairment in the elderly causes a significant decline in the quality of life and a substantial economic burden on society. Yet, diagnosing cognitive impairment is apt to be missed or delayed due to its assessment being laborious. This study aimed to propose a new approach of classifying the risk of cognitive impairment in the elderly using sequential gait characteristics and machine learning techniques. A total of 108 community-dwelling elderly individuals participated in this study. The participants were categorized into three groups based on their scores of the mini-mental state examination. Each participant completed both the usual- and fast-paced walking on the straight path with two gyroscopes on each foot. By analyzing the foot sagittal angular velocity signals, the temporal gait parameters were extracted from each gait cycle. Five classical machine learning models and a long short-term memory network were respectively employed to produce the classifiers that used the time-consecutive temporal gait parameters as predictors of cognitive impairment. Five-fold cross-validation was applied to 70% of the data in each group, and the remaining 30% were used as test data. An F1-score of 0.974 was achieved in classifying the three groups by the long short-term memory network-based classifier that used the double-limb support, stance, step, and stride times at usual-paced walking and the double- and single-limb support, stance, and stride times at fast-paced walking as inputs. The proposed approach would pave the way for earlier diagnosis of cognitive impairment in non-clinical settings without professional help, which can facilitate more timely intervention.