Accurate human motion prediction is crucial for safe human-robot collaboration but remains challenging due to the complexity of modeling intricate and variable human movements. This paper presents Parallel Multi-scale Incremental Prediction (PMS), a novel framework that explicitly models incremental motion across multiple spatio-temporal scales to capture subtle joint evolutions and global trajectory shifts. PMS encodes these multi-scale increments using parallel sequence branches, enabling iterative refinement of predictions. A multi-stage training procedure with a full-timeline loss integrates temporal context. Extensive experiments on four datasets demonstrate substantial improvements in continuity, biomechanical consistency, and long-term forecast stability by modeling inter-frame increments. PMS achieves state-of-the-art performance, increasing prediction accuracy by 16.3%-64.2% over previous methods. The proposed multi-scale incremental approach provides a powerful technique for advancing human motion prediction capabilities critical for seamless human-robot interaction.