A target for a high-brightness microfocus x-ray tube, which is based on carbon nanotubes (CNT) as electron source, is designed. The x-ray tube has the following specifications: brightness of $1 X 10^{11} ph/s-㎟mrad^2$, spot size ~ 5㎛, and average x-ray energy of 20~40 keV. In order to satisfy the specifications, the design parameters of the target, such as configuration, material, thickness of the target as well as the required beam current, were optimized using computer code MCNPX. The design parameters were determined from the calculation of both x-ray spectrum and intensity distribution. From the calculation, transmission type was chosen for the target configuration. The material of the target was selected as molybdenum (Mo) and the optimized thickness was 7.2㎛ . Since such a thin target should withstand vacuum pressure and localized thermal loading, structural stability and temperature distribution were also considered. According to the analytic calculation, the transmission Mo target itself could not withstand the vacuum pressure. An alternative is to use backing material of 150㎛ beryllium (Be) on the backside of the Mo target. In addition, the calculation shows that the maximum temperature of the transmission target can be reduced to a stable-operation regime by forced air-convection cooling.