Due to the fast growth of the market for personal mobile devices and the improvement of process technology, more and more multi-media applications are embedded on our handheld devices. Since most of these devices use the screen as its main user interface, high visual quality becomes one of the most important factors when evaluating the user experience. To achieve this requirement, GPU becomes a great computing power for a mobile device. However, the mobile devices may not have enough power due to the nature of sparse resource. For example, the only power supply for mobile phone is the battery. Therefore, it is a big challenge to maintain visual quality under a low battery situation. In this thesis, we proposed a low power graphics pipeline based on approximate rendering technique with error control scheme. The approximate rendering technique is targeting on reducing the number of rendered pixel and hence to reduce the expensive computation power. The proposed technique can reach a reduction rate of 50% for medium resolution mode and 80% for low resolution mode in most cases. Furthermore, the error control scheme can estimate the error caused by the approximation so the system can render objects adaptively. Consequently the error control scheme, we can render image with fewer pixels but still sustain acceptable quality. Finally, with the proposed techniques above, a multi-core GPU system for mobile devices is implemented. The prototype chip is fabricated in TSMC 65nm technology, and the chip size is 4.0o4.0mm2. The designed working requency is 200MHz, and the worst case power consumption is 128mW.