Current host-centric Internet Protocol (IP) networks are facing unprecedented challenges, such as network attacks and the exhaustion of IP addresses. Motivated by emerging demands for security, mobility, and distributed networking, many research projects have been initiated to design the future Internet from a clean slate. In order to obtain a thorough knowledge of security in future Internet architecture, we review a number of well-known projects, including named data networking, Content Aware Searching Retrieval and sTreaming, MobilityFirst Future Internet Architecture Project (MobilityFirst), eXpressive Internet Architecture, and scalability, control, and isolation on next-generation network. These projects aim to move away from the traditional host-centric networks and replace them with content-centric, mobility-centric, or service-centric networks. However, different principles and designs also raise various issues on network security. For each project, we describe its architecture design and how it deals with security issues. Furthermore, we compare these projects and discuss their pros and cons. Open security issues are pointed out for directing future research.