Wireless Sensor Networks (WSNs) have application in a variety of fields including inhospital locations, military purposes, transportation automation, home and industrial automation. WSNs also are used in monitoring synchronous or asynchronous events that require periodic data collection. WSNs consist of a large number small device or Wireless Nodes (WNs) and are responsible for sensing, collecting, processing and monitoring information of real world environments. WSNs consist of a Data Acquisition Network (DAN) and a Data distribution Network (DDN) which monitored and controlled by a management center. The primary limiting factor for the lifetime of a WSN is the power supply. Regarding the applications of WSNs it is often impossible to obtain physical access to replace or charge battery. Therefore we can design low power WSNs. In WSNs, the events are sparse signal compared with the number of sources. That is why; the compressed sensing theory holds promising to reduce power consumption. Compressed Sensing shows that spars signals such as signals of WSNs can be exactly reconstructed from a small number of random linear measurements. Compressed Sensing theory can reduce number of bits information through whole of the network and consequently decrease amount of current that drawn from power supply. With this in mind, we introduce a new mechanism to design low-power WSN with compressed sensing theory. This paper gives a background of compressed sensing theory, and then describes important concepts in wireless sensor networks, and finally our simulation by applying compressed sensing in WSNs theory is described.