Internet of Things applications encompass home-automation, health, transportation, etc. The main objective of these applications is to improve user's daily lives. However, security and privacy threats and the lack of adapted security mechanisms could significantly reduce their development and slow-down their adoption. Several researches have been conducted in order to find solutions for securing the IoT systems and to reduce, even eliminate risks for user's privacy. One of the proposed solutions is context-aware security, which enables to consider relevant contextual information while implementing security mechanisms. In this paper, we will conduct a survey of the context-aware security solutions that have been proposed for smart city IoT applications. These applications have a great impact on citizens life. For each solution, we will provide critical analysis in terms of context-aware management, security services and privacy mechanisms. Then, we will identify the different research directions for better context-aware security in these applications.