A lensless camera is an imaging system that uses a mask in place of a lens, making it thinner, lighter, and less expensive than a lensed camera. However, additional complex computation and time are required for image reconstruction. This work proposes a deep learning model named Raw3dNet that recognizes hand gestures directly on raw videos captured by a lensless camera without the need for image restoration. In addition to conserving computational resources, the reconstruction-free method provides privacy protection. Raw3dNet is a novel end-to-end deep neural network model for the recognition of hand gestures in lensless imaging systems. It is created specifically for raw video captured by a lensless camera and has the ability to properly extract and combine temporal and spatial features. The network is composed of two stages: 1. spatial feature extractor (SFE), which enhances the spatial features of each frame prior to temporal convolution; 2. 3D-ResNet, which implements spatial and temporal convolution of video streams. The proposed model achieves 98.59% accuracy on the Cambridge Hand Gesture dataset in the lensless optical experiment, which is comparable to the lensed-camera result. Additionally, the feasibility of physical object recognition is assessed. Further, we show that the recognition can be achieved with respectable accuracy using only a tiny portion of the original raw data, indicating the potential for reducing data traffic in cloud computing scenarios.