Survival analysis aims to predict the occurrence time of a particular event of interest, which is crucial for the prognosis analysis of diseases. Currently, due to the limited study period and potential losing tracks, the observed data inevitably involve some censored instances, and thus brings a unique challenge that distinguishes from the general regression problems. In addition, survival analysis also suffers from other inherent challenges such as the high-dimension and small-sample-size problems. To address these challenges, we propose a novel multi-task regression learning model, i.e., prior information guided transductive matrix completion (PigTMC) model, to predict the survival status of the new instances. Specifically, we use the multi-label transductive matrix completion framework to leverage the censored instances together with the uncensored instances as the training samples, and simultaneously employ the multi-task transductive feature selection scheme to alleviate the overfitting issue caused by high-dimension and small-sample-size data. In addition, we employ the prior temporal stability of the survival statuses at adjacent time intervals to guide survival analysis. Furthermore, we design an optimization algorithm with guaranteed convergence to solve the proposed PigTMC model. Finally, the extensive experiments performed on the real microarray gene expression datasets demonstrate that our proposed model outperforms the previously widely used competing methods.