Large language model-powered code agents are rapidly transforming software engineering, yet the security risks of their generated code have become a critical concern. Existing benchmarks have provided valuable insights, but they fail to capture scenarios in which vulnerabilities are actually introduced by human developers, making fair comparisons between humans and agents infeasible. We therefore introduce SecureVibeBench, a benchmark of 105 C/C++ secure coding tasks sourced from 41 projects in OSS-Fuzz for code agents. SecureVibeBench has the following features: (i) realistic task settings that require multi-file edits in large repositories, (ii)~aligned contexts based on real-world open-source vulnerabilities with precisely identified vulnerability introduction points, and (iii) comprehensive evaluation that combines functionality testing and security checking with both static and dynamic oracles. We evaluate 5 popular code agents like OpenHands, supported by 5 LLMs (e.g., Claude sonnet 4.5) on SecureVibeBench. Results show that current agents struggle to produce both correct and secure code, as even the best-performing one, produces merely 23.8\% correct and secure solutions on SecureVibeBench. Our code and data are on https://github.com/iCSawyer/SecureVibeBench.