Contrastive cross-modality pretraining has recently exhibited impressive success in diverse fields, whereas there is limited research on their merits in speech emotion recognition (SER). In this paper, we propose GEmo-CLAP, a kind of gender-attribute-enhanced contrastive language-audio pretraining (CLAP) method for SER. Specifically, we first construct an effective emotion CLAP (Emo-CLAP) for SER, using pre-trained text and audio encoders. Second, given the significance of gender information in SER, two novel multi-task learning based GEmo-CLAP (ML-GEmo-CLAP) and soft label based GEmo-CLAP (SL-GEmo-CLAP) models are further proposed to incorporate gender information of speech signals, forming more reasonable objectives. Experiments on IEMOCAP indicate that our proposed two GEmo-CLAPs consistently outperform Emo-CLAP with different pre-trained models. Remarkably, the proposed WavLM-based SL-GEmo-CLAP obtains the best WAR of 83.16\%, which performs better than state-of-the-art SER methods.