The continuous evolution of pre-trained speech models has greatly advanced Speech Emotion Recognition (SER). However, current research typically relies on utterance-level emotion labels, inadequately capturing the complexity of emotions within a single utterance. In this paper, we introduce GMP-TL, a novel SER framework that employs gender-augmented multi-scale pseudo-label (GMP) based transfer learning to mitigate this gap. Specifically, GMP-TL initially uses the pre-trained HuBERT, implementing multi-task learning and multi-scale k-means clustering to acquire frame-level GMPs. Subsequently, to fully leverage frame-level GMPs and utterance-level emotion labels, a two-stage model fine-tuning approach is presented to further optimize GMP-TL. Experiments on IEMOCAP show that our GMP-TL attains a WAR of 80.0% and an UAR of 82.0%, achieving superior performance compared to state-of-the-art unimodal SER methods while also yielding comparable results to multimodal SER approaches.