Implicit Discourse Relation Recognition (IDRR) is to detect and classify relation sense between two text segments without an explicit connective. Vanilla pre-train and fine-tuning paradigm builds upon a Pre-trained Language Model (PLM) with a task-specific neural network. However, the task objective functions are often not in accordance with that of the PLM. Furthermore, this paradigm cannot well exploit some linguistic evidence embedded in the pre-training process. The recent pre-train, prompt, and predict paradigm selects appropriate prompts to reformulate downstream tasks, so as to utilizing the PLM itself for prediction. However, for its success applications, prompts, verbalizer as well as model training should still be carefully designed for different tasks. As the first trial of using this new paradigm for IDRR, this paper develops a Connective-cloze Prompt (ConnPrompt) to transform the relation prediction task as a connective-cloze task. Specifically, we design two styles of ConnPrompt template: Insert-cloze Prompt (ICP) and Prefix-cloze Prompt (PCP) and construct an answer space mapping to the relation senses based on the hierarchy sense tags and implicit connectives. Furthermore, we use a multi-prompt ensemble to fuse predictions from different prompting results. Experiments on the PDTB corpus show that our method significantly outperforms the state-of-the-art algorithms, even with fewer training data.