In recent years, the demand for portable radio communication has been increasing which requires low profile, light weight and small size antennas. Therefore, the size of the antenna is required to be as small as possible. In this thesis, some of the compact antennas will be analyzed and simulated. The early-stage PIFA antenna will be investigated first, and then the shorting pin characteristics to design compact and dual band antenna was utilized. Because the shorting pin will lead to the decrease of bandwidth, replacement of the shorting pin by using chip-resistor could improve this characteristic. The compactness of antennas will lead to the decrease of the gain. In order to improve the gain of antennas, the combination of substrate and superstrate configuration with very high permittivity material is used. For the consideration of Bluetooth system, we use the ACPS (Asymmetrical Co-planar Striplines) structure to design the antenna. Using this structure in the design will obtain a promotion in bandwidth compared with the conventional rectangular microstrip antenna. Because the size of the antenna is small, the time to simulate this structure by the FDTD (Finite Difference Time Domain) method is too long. In order to solve this problem, this thesis mainly study a new FDTD algorithm based on the Alternating-Direction Implicit method, and use this algorithm to simulate some simple structures.