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Wearable sensor-based Human Action Recognition (HAR) has achieved remarkable success recently. However, the accuracy performance of wearable sensor-based HAR is still far behind the ones from the visual modalities-based system (i.e., RGB video, skeleton, and depth). Diverse input modalities can provide complementary cues and thus improve the accuracy performance of HAR, but how to take advantage of multi-modal data on wearable sensor-based HAR has rarely been explored. Currently, wearable devices, i.e., smartwatches, can only capture limited kinds of non-visual modality data. This hinders the multi-modal HAR association as it is unable to simultaneously use both visual and non-visual modality data. Another major challenge lies in how to efficiently utilize multimodal data on wearable devices with their limited computation resources. In this work, we propose a novel Progressive Skeleton-to-sensor Knowledge Distillation (PSKD) model which utilizes only time-series data, i.e., accelerometer data, from a smartwatch for solving the wearable sensor-based HAR problem. Specifically, we construct multiple teacher models using data from both teacher (human skeleton sequence) and student (time-series accelerometer data) modalities. In addition, we propose an effective progressive learning scheme to eliminate the performance gap between teacher and student models. We also designed a novel loss function called Adaptive-Confidence Semantic (ACS), to allow the student model to adaptively select either one of the teacher models or the ground-truth label it needs to mimic. To demonstrate the effectiveness of our proposed PSKD method, we conduct extensive experiments on Berkeley-MHAD, UTD-MHAD, and MMAct datasets. The results confirm that the proposed PSKD method has competitive performance compared to the previous mono sensor-based HAR methods.