Systems of sensor human activity recognition are becoming increasingly popular in diverse fields such as healthcare and security. Yet, developing such systems poses inherent challenges due to the variations and complexity of human behaviors during the performance of physical activities. Recurrent neural networks, particularly long short-term memory have achieved promising results on numerous sequential learning problems, including sensor human activity recognition. However, parallelization is inhibited in recurrent networks due to sequential operation and computation that lead to slow training, occupying more memory and hard convergence. One-dimensional convolutional neural network processes input temporal sequential batches independently that lead to effectively executed operations in parallel. Despite that, a one-dimensional Convolutional Neural Network is not sensitive to the order of the time steps which is crucial for accurate and robust systems of sensor human activity recognition. To address this problem, we propose a network architecture based on dilated causal convolution and multi-head self-attention mechanisms that entirely dispense recurrent architectures to make efficient computation and maintain the ordering of the time steps. The proposed method is evaluated for human activities using smart home binary sensors data and wearable sensor data. Results of conducted extensive experiments on eight public and benchmark HAR data sets show that the proposed network outperforms the state-of-the-art models based on recurrent settings and temporal models.