Recently, modern smartphones equipped with a variety of embedded-sensors, such as accelerometers and gyroscopes, have been used as an alternative platform for human activity recognition (HAR), since they are cost-effective, unobtrusive and they facilitate real-time applications. However, the majority of the related works have proposed a position-dependent HAR, i.e., the target subject has to fix the smartphone in a pre-defined position. Few studies have tackled the problem of position-independent HAR. They have tackled the problem either using handcrafted features that are less influenced by the position of the smartphone or by building a position-aware HAR. The performance of these studies still needs more improvement to produce a reliable smartphone-based HAR. Thus, in this paper, we propose a deep convolution neural network model that provides a robust position-independent HAR system. We build and evaluate the performance of the proposed model using the RealWorld HAR public dataset. We find that our deep learning proposed model increases the overall performance compared to the state-of-the-art traditional machine learning method from 84% to 88% for position-independent HAR. In addition, the position detection performance of our model improves superiorly from 89% to 98%. Finally, the recognition time of the proposed model is evaluated in order to validate the applicability of the model for real-time applications.