Abstarct: Today, with the development of devices and equipment that works with batteries, and due to the limitation of battery lifetimes, the use of wireless power transmission systems to remove batteries, as well as the elimination of physical connections, such as wires for greater convenience, are very much considered. The applications of such systems can be noted to the charge of cell phones, laptops, electric vehicles and using in medical implants fields. In this thesis, using the idea of power transfer by multiband systems, and with regard to many benefits that can be defined for them, a dual-band wireless power transfer system is designed and manufactured to improve the power output at frequencies of 6.78 MHz and 13.56 MHz. In this regard, dual-band planar resonators are used as the power transmitter and receiver, and the source and load coils are applied as transformer matching networks, as well as an analytical relation are presented for the power transfer efficiency of the system. It will be shown analytically, for each of the operating frequency, with different values of the inductance of external coils, there are certain critical coupling coefficients between the external coils and internal resonators that the impedance matching has occurred, and by selecting the appropriate coupling coefficient close to the critical coupling coefficients of both bands, the maximum power can be transmitted through each frequency bands. Finally, the measurement results show the efficiency of 71% and 56% at the frequencies of 6.78 MHz and 13.56 MHz, respectively, where are in agreement with the simulation results.