Due to the absence of connectives, implicit discourse relation recognition (IDRR) is still a challenging and crucial task in discourse analysis. Most of the current work adopted multitask learning to aid IDRR through explicit discourse relation recognition (EDRR) or utilized dependencies between discourse relation labels to constrain model predictions. But these methods still performed poorly on fine-grained IDRR and even utterly misidentified on most of the few-shot discourse relation classes. To address these problems, we propose a novel Prompt-based Connective Prediction (PCP) method for IDRR. Our method instructs large-scale pre-trained models to use knowledge relevant to discourse relation and utilizes the strong correlation between connectives and discourse relation to help the model recognize implicit discourse relations. Experimental results show that our method surpasses the current state-of-the-art model and achieves significant improvements on those fine-grained few-shot discourse relation. Moreover, our approach is able to be transferred to EDRR and obtain acceptable results. Our code is released in https://github.com/zh-i9/PCP-for-IDRR.