A transmitter coil (TX-coil) as well as a receiver coil (RX-coil) has been designed at 6.78 MHz for magnetic resonant wireless power transfer systems not only to have high efficiency at medium distances, which is comparable to the coil dimensions, but also to provide stable efficiency over the position variation of the RX-coil. For mobile devices, the coils should be compact and have low profile and asymmetric, meaning that TX- and RX-coils have different dimensions. In this paper, TX-coil is designed by adding a small coil in series to achieve high quality factor (Q-factor) as well as relatively uniform magnetic field distribution. On the other hand, the scaling factor is introduced for wire width to design RX-coil with higher Q-factor. As a result, the proposed asymmetric coils reveal improved efficiency and degree of freedom in terms of position variation. This has been verified by measuring the system performance, including a power amplifier, full-wave rectifier, regulator, and load. The proposed TX-coil has size of $200 \times 200 \times 1$ mm3, while the size of the RX-coil is $100\times 100\times0.4$ mm3. The power transfer efficiency is 96% and 39% at the transmission distances of 50 and 300 mm, respectively.