This paper presents an application-specific processor for the transformation and tessellation operations in 2D graphics front-end rendering process. In order to accelerate the curve tessellation, this processor utilizes a dedicated cubic bezier-curve (CBC) unit based on the modified adaptive forwarddifference (FD) algorithm to efficiently locate the intersection points of a curve with all the scan-lines. In addition, the processor's main arithmetic unit can support the value lookup of several special arithmetic functions in order to fasten the transform operations. Our preliminary results show that our processor consumes less than 200k gates, and can achieve the rendering speed of more than 60 frames per second (fps) for several major benchmarks in QCIF resolution. Since the proposed processor is programmable, it can be further extended easily to support more complex graphics effects in future.