Point cloud frame interpolation is a challenging task that involves accurate scene flow estimation across frames and maintaining the geometry structure. Prevailing techniques often rely on pre-trained motion estimators or intensive testing-time optimization, resulting in compromised interpolation accuracy or prolonged inference. This work presents FastPCI that introduces Pyramid Convolution-Transformer architecture for point cloud frame interpolation. Our hybrid Convolution-Transformer improves the local and long-range feature learning, while the pyramid network offers multilevel features and reduces the computation. In addition, FastPCI proposes a unique Dual-Direction Motion-Structure block for more accurate scene flow estimation. Our design is motivated by two facts: (1) accurate scene flow preserves 3D structure, and (2) point cloud at the previous timestep should be reconstructable using reverse motion from future timestep. Extensive experiments show that FastPCI significantly outperforms the state-of-the-art PointINet and NeuralPCI with notable gains (26.6% and 18.3% reduction in Chamfer Distance in KITTI), while being more than 10x and 600x faster, respectively.