Today, with the advancement of technology, Internet usage is increased while there are some limitations for using the free frequency band. Furthermore, in many cases, the licensed frequency band are not used by their primary users. In this way, there are opportunities for unlicensed users which are equipped with cognitive radio technology to use such licensed frequency bands. Some specific secondary users can be the wireless sensors. The specific property of the wireless sensor networks is the application of these networks such as controlling, checking accident-prone areas and military attentions. The secondary users are required to sense the spectrum continuously, to prevent the interference with the primary user. The spectrum sensing for cognitive radio network with the mobile primary user is different with those in which the primary user has no mobility. For a mobile primary user, a secure region is defined such that the secondary users in that region can transmit data if primary user is not present in the spectrum. In this case, when the location of the primary user is changed, the secondary users which are able to sense the spectrum are changed, too. Other sensors which are located outside of the secure region of the primary user and do not participate on the spectrum sensing can send their data and use the licensed spectrum band. If the radius of the secure region is short, the number of times that sensors can use the spectrum without any interference will increase. Since sensors in a cognitive radio network have limited battery life, the way of their energy consumption is of importance. To the best of our knowledge, the existing researches have considered spectrum sensing methods with the presence of mobile primary user. However, there is a lack of research in which the energy consumption of sensors with mobile primary user is studied. Therefore, in this thesis a new analytical framework is proposed to demonstrate how sensors consume their energy in a cognitive radio networks with a mobile primary user. Using the proposed analytical framework as well as simulation, the effect of the secure region radius of the primary user on the detection probability, transmission probability and energy consumption for the spectrum sensing have been studied. Results from simulation have good agreement with those from analysis. Keywords: Wireless sensor cognitive radio networks, mobile primary user, energy consumption, interference reduction