RNA sequencing has emerged as a promising approach in cancer prognosis as sequencing data becomes more easily and affordably accessible. However, it remains challenging to build good predictive models especially when the sample size is limited and the number of features is high, which is a common situation in biomedical settings. To address these limitations, we propose a meta-learning framework based on neural networks for survival analysis and evaluate it in a genomic cancer research setting. We demonstrate that, compared to regular transfer-learning, meta-learning is a significantly more effective paradigm to leverage high-dimensional data that is relevant but not directly related to the problem of interest. Specifically, meta-learning explicitly constructs a model, from abundant data of relevant tasks, to learn a new task with few samples effectively. For the application of predicting cancer survival outcome, we also show that the meta-learning framework with a few samples is able to achieve competitive performance with learning from scratch with a significantly larger number of samples. Finally, we demonstrate that the meta-learning model implicitly prioritizes genes based on their contribution to survival prediction and allows us to identify important pathways in cancer.