High performance 3D graphics processor is one of the most important hardware modules in modern mobile SoC design. This paper presents the design of a fully programmable 3D graphics processor taking advantage of unified shader architecture for mobile applications. We adopt multi-thread scheduling to utilize data, instruction parallelism and reduce data dependency stalls. In the unified shader core design, we adopt single instruction multiple data (SIMD) architecture to support four concurrent scalar operation. Moreover, we propose a novel special function unit for floating point transcendental function computation. Using these optimization methods, the proposed mobile 3D graphics processor achieves vertex and fragment processing speed of 600M/s under 40nm technology.