In internet of things (IoT) paradigm, crowdsourcing is the process of obtaining and analyzing information or input to a particular task or project generated by a number of sources such as sensors, mobile devices, vehicles and human. Cloud computing is widely used for the services such as analyzing crowdsourced data and application implementation over the IoT. Nowadays, every country and human are prone to natural and artificial disasters. Early detection about disasters such as earthquakes, fire, storms, and floods can save thousands of people’s life and effective preventive measure can be taken for the public safety. All the crowdsourced data which are providing the information of a certain geographic region are analyzed in a cloud platform. But, by the time the crowdsourced data makes its way to the cloud for analysis, the opportunity to act on it might be gone. Moreover, thousands of people’s life will be lost. Therefore, fog computing is the new and efficient way to analyze such critical crowdsourced IoT data of disasters. In this paper, in order to detect and take necessary steps for public safety during a disaster, we propose a crowdsourcing-based disaster management using fog computing (CDMFC) model in IoT. Further, we also proposed a data offloading mechanism for our CDMFC model to send disaster-related IoT data to the fog even if a direct link to the fog is not available. Our proposed CDMFC model and its data offloading mechanism can detect real-time disasters and disseminate early information for public safety as compared to the conventional cloud computing based disaster management models.