Human activity recognition (HAR) based on multi-modal approach has been recently shown to improve the accuracy performance of HAR. However, restricted computational resources associated with wearable devices, i.e., smartwatch, failed to directly support such advanced methods. To tackle this issue, this study introduces an end-to-end Vision-to-Sensor Knowledge Distillation (VSKD) framework. In this VSKD framework, only time-series data, i.e., accelerometer data, is needed from wearable devices during the testing phase. Therefore, this framework will not only reduce the computational demands on edge devices, but also produce a learning model that closely matches the performance of the computational expensive multi-modal approach. In order to retain the local temporal relationship and facilitate visual deep learning models, we first convert time-series data to two-dimensional images by applying the Gramian Angular Field (GAF) based encoding method. We adopted ResNet18 and multi-scale TRN with BN-Inception as teacher and student network in this study, respectively. A novel loss function, named Distance and Angle-wised Semantic Knowledge loss (DASK), is proposed to mitigate the modality variations between the vision and the sensor domain. Extensive experimental results on UTD-MHAD, MMAct and Berkeley-MHAD datasets demonstrate the effectiveness and competitiveness of the proposed VSKD model which can deployed on wearable sensors.