Recent radar-based human activity recognition (HAR) researches focus on time-Doppler images in one particular range bin. However, image-based methods suffer from low representation efficiency, and analysis in one range bin results in information loss for non-in-place motions. This paper proposes a novel radar-based HAR with range-distributed time-Doppler sparse point cloud (RTDSP) and multi-channel PointNet to address this issue. First, sparsity-based features are extracted as a limited number of sparse points to characterize human activities in the time-Doppler domain. Next, it is extended to motion-distributed range bins to obtain a range sequence of the time-Doppler sparse point cloud as RTDSP features. Then, multichannel PointNet is designed to learn multi-domain features from RTDSP for classification. Finally, comprehensive experiments were conducted to demonstrate its feasibility and superiority by achieving an average accuracy rate of 97.0% in recognizing six typical daily human activities.