Cancer prognosis and survival outcome predictions are crucial for therapeutic response estimation and for stratifying patients into various treatment groups. Medical domains concerned with cancer prognosis are abundant with multiple modalities, including pathological image data and non-image data such as genomic information. To date, multimodal learning has shown potential to enhance clinical prediction model performance by extracting and aggregating information from different modalities of the same subject. This approach could outperform single modality learning, thus improving computer-aided diagnosis and prognosis in numerous medical applications. In this work, we propose a cross-modality attention-based multimodal fusion pipeline designed to integrate modality-specific knowledge for patient survival prediction in non-small cell lung cancer (NSCLC). Instead of merely concatenating or summing up the features from different modalities, our method gauges the importance of each modality for feature fusion with cross-modality relationship when infusing the multimodal features. Compared with single modality, which achieved c-index of 0.5772 and 0.5885 using solely tissue image data or RNA-seq data, respectively, the proposed fusion approach achieved c-index 0.6587 in our experiment, showcasing the capability of assimilating modality-specific knowledge from varied modalities.