Effective motion estimation is one of the prime steps for any human action recognition (HAR) algorithm. Optical flow (OF) and motion history image (MHI) are two well-known methods for motion estimation in videos. OF has several advantages over MHI. But the major drawback with OF is that it is computationally very expensive as compared to the MHI. Therefore, in this paper, a new motion estimation technique named as Weber Motion History Image (WMHI) is proposed. Here, an extremely fast algorithm is proposed for HAR using WMHI, pose information, and convolutional neural network (CNN). In spite of being fast and less space consuming, the algorithm outperforms the existing pose based CNN results on five benchmark datasets namely JHMDB [1], sub-JHMDB [1], MPII [2] and HMDB51 [3] and UCF101 [4]. The work mainly focuses on a new efficient algorithm which can be implemented for real-time HAR in videos. For real-time implementation, the two basic criteria on which an algorithm can be analyzed are space and time complexity. The proposed algorithm is faster as compared to the existing OF based HAR systems. In terms of space complexity, the feature size of the proposed algorithm is almost 50% of the existing OF based algorithm. The recognition results still outperform the existing result by a significant margin.