We propose a novel video sampling scheme for human action recognition in videos, using Gaussian Weighing Function. Traditionally in deep learning-based human activity recognition approaches, either a few random frames or every $k^{th}$ frame of the video is considered for training the 3D CNN, where $k$ is a small positive integer, like $4$, $5$, or $6$. This kind of sampling reduces the volume of the input data, which speeds-up the training network and also avoids overfitting to some extent, thus enhancing the performance of the 3D CNN model. In the proposed video sampling technique, consecutive $k$ frames of a video are aggregated into a single frame by computing a Gaussian-weighted summation of the $k$ frames. The resulting frame preserves the information in a better way than the conventional approaches and experimentally shown to perform better. In this paper, a 3-Dimensional deep CNN is proposed to extract the spatio-temporal features and follows Long Short-Term Memory (LSTM) to recognize human actions. The proposed 3D CNN architecture is capable of handling the videos where the camera is placed at a distance from the performer. Experiments are performed with KTH, WEIZMANN, and CASIA-B Human Activity and Gait datasets, whereby it is shown to outperform state-of-the-art deep learning based techniques. We achieve 95.78%, 95.27%, and 95.27% over the KTH, WEIZMANN, and CASIA-B human action and gait recognition datasets, respectively.