The Internet of Things (IoT) networks are vulnerable to various kinds of attacks, being the sinkhole attack one of the most destructive since it prevents communication among network devices. In general, existing solutions are not effective to provide protection and security against attacks sinkhole on IoT, and they also introduce high consumption of resources de memory, storage and processing. Further, they do not consider the impact of device mobility, which in essential in urban scenarios, like smart cities. This paper proposes an intrusion detection system, called INTI (Intrusion detection of SiNkhole attacks on 6LoWPAN for InterneT of ThIngs), to identify sinkhole attacks on the routing services in IoT. Moreover, INTI aims to mitigate adverse effects found in IDS that disturb its performance, like false positive and negative, as well as the high resource cost. The system combines watchdog, reputation and trust strategies for detection of attackers by analyzing the behavior of devices. Results show the INTI performance and its effectiveness in terms of attack detection rate, number of false positives and false negatives.