Accurately predicting the survival of patients with esophageal cancer after esophagectomy is crucial for clinical precision treatment. However, the existing methods of predicting Overall Survival time (OStime) mostly build supervised learning with the uncensored data, ignoring the potential information hidden in the censored data. To utilize the information hidden in the clinically abundant censored data, we propose a Semi-Supervised Learning with Adaptive pseudo-label Selection and Correction (SSLASC) to predict the OStime of esophageal cancer using both uncensored and censored data. Specifically, we first transform the OStime regression problem to a classification task followed by Softmax Expected Value Refinement (SEVR) and train a Transformer network using the uncensored data, which is then used to predict the OStime for the censored data. Secondly, we design an adaptive pseudo-label selection strategy to dynamically select more classes and more balanced samples from the predicted censored data by allocating adaptive thresholds for different classes of samples when performing pseudo-label selection. Finally, a distribution correction and a meta label correction modules are proposed to make the selected pseudo-labels closer to the real overall OStime. We test SSLASC on an internal dataset and two external datasets with sample sizes of 327, 104, and 16, respectively. The experimental results demonstrate that SSLASC achieves Mean Absolute Error (MAE) of 12.23, 12.64, and 12.47 months on the three test datasets. Compared to the optimal State-Of-The-Art (SOTA) method, SSLASC improves performance by 1.09, 1.07, and 1.09 months, respectively. In addition, SSLASC also achieves the best performance in dichotomized survival analysis.