As a crucial building block in vertical Federated Learning (vFL), Split Learning (SL) has demonstrated its practice in the two-party model training collaboration, where one party holds the features of data samples and another party holds the corresponding labels. Such method is claimed to be private considering the shared information is only the embedding vectors and gradients instead of private raw data and labels. However, some recent works have shown that the private labels could be leaked by the gradients. These existing attack only works under the classification setting where the private labels are discrete. In this work, we step further to study the leakage in the scenario of the regression model, where the private labels are continuous numbers (instead of discrete labels in classification). This makes previous attacks harder to infer the continuous labels due to the unbounded output range. To address the limitation, we propose a novel learning-based attack that integrates gradient information and extra learning regularization objectives in aspects of model training properties, which can infer the labels under regression settings effectively. The comprehensive experiments on various datasets and models have demonstrated the effectiveness of our proposed attack. We hope our work can pave the way for future analyses that make the vFL framework more secure.