In this paper, we present theoretical analysis and detailed design of a class of wireless power transfer (WPT) systems based on strong coupled magnetic resonances. We established the strong coupled resonance conditions for practically implementable WPT systems. We investigated the effects of non-ideal conditions presented in most practical systems on power transfer efficiency and proposed solutions to deal with these problems. We carried out a design of WPT system by using PCB (Printed Circuit Board) antenna pair, which showed strong coupled magnetic resonances. The innovations of our design include: (1) a new coil winding pattern for resonant coils that achieves a compact space volume, (2) fabrication of resonant coils on PCBs, and (3) integration of the entire system on a pair of PCBs. Extensive experiments were performed and experimental results showed that our WPT system setup achieved a guaranteed power transfer efficiency 14% over a distance of two times characteristic length(44cm). The wireless power transfer efficiency in this PCB based experimental system was sufficiently high to lighten up a LED with a signal generator.