Software vulnerabilities are code segments in software that are prone to exploitation. Ensuring that software is not easily attacked is a crucial security requirement in software development. Software vulnerability prediction involves analyzing and predicting potential vulnerabilities in software code. Deep learning-driven software vulnerability prediction has become a popular research field in recent years, with a long time span, numerous studies, and substantial research achievements. To review relevant research findings and summarize the research hotspots, a survey of 151 studies related to deep learning-driven software vulnerability prediction published between 2017 and 2024 is conducted. It summarizes the research problems, progress, and challenges discussed in the literature, providing a reference for future research.