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Recently, deep learning has represented an important research trend in human activity recognition (HAR). In particular, deep convolutional neural networks (CNNs) have achieved state-of-the-art performance on various HAR datasets. For deep learning, improvements in performance have to heavily rely on increasing model size or capacity to scale to larger and larger datasets, which inevitably leads to the increase of operations. A high number of operations in deep leaning increases computational cost and is not suitable for real-time HAR using mobile and wearable sensors. Though shallow learning techniques often are lightweight, they could not achieve good performance. Therefore, deep learning methods that can balance the trade-off between accuracy and computation cost is highly needed, which to our knowledge has seldom been researched. In this paper, we for the first time propose a computation efficient CNN using conditionally parametrized convolution for real-time HAR on mobile and wearable devices. We evaluate the proposed method on four public benchmark HAR datasets consisting of WISDM dataset, PAMAP2 dataset, UNIMIB-SHAR dataset, and OPPORTUNITY dataset, achieving state-of-the-art accuracy without compromising computation cost. Various ablation experiments are performed to show how such a network with large capacity is clearly preferable to baseline while requiring a similar amount of operations. The method can be used as a drop-in replacement for the existing deep HAR architectures and easily deployed onto mobile and wearable devices for real-time HAR applications.