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In recent years, sensor-based human activity recognition (HAR) has gained tremendous attention around the world with a range of applications. Instead of using body sensor network-based recognition systems which are intrusive and increase equipment cost, we focus on the development of efficient HAR approach based on a single triaxial accelerometer. In order to improve the recognition accuracy of the system, a novel recognition approach based on kernel discriminant analysis (KDA) and quantum-behaved particle swarm optimization-based kernel extreme learning machine (QPSO-KELM) is proposed. KDA is utilized to extract more meaningful features and enhance the discrimination between different activities. To verify the effectiveness of KDA, three kinds of features including original features, linear discriminant analysis (LDA) features and KDA features are extracted and compared for activity recognition. In addition, QPSO-KELM is compared with two existing classification methods: support vector machine (SVM) and extreme learning machine (ELM), which are commonly utilized in activity recognition. Meanwhile, two comparative optimization methods for KELM are also discussed in the experiment. The experimental results demonstrate the superiority of the proposed approach.