Scientific computations for diffusion equations and ANNs (Artificial Neural Networks) are data intensive tasks accompanied by heavy memory access; on the other hand, their computational complexities are relatively low. Thus, this type of tasks naturally maps onto SIMD (Single Instruction Multiple Data stream) parallel processing with distributed memory. This paper proposes a high performance acceleration processor of which architecture is optimized for scientific computing using diffusion equations and ANNs. The proposed architecture includes a customized instruction set and specific hardware resources which consist of a control unit (CU), 16 processing units (PUs), and a non-linear function unit (NFU) on chip. They are effectively connected with dedicated ring and global bus structure. Each PU is equipped with an address modifier (AM) and 16-bit 1.5 k-word local memory (LM). The proposed processor can be easily expanded by multi-chip expansion mode to accommodate to a large scale parallel computation. The prototype chip is implemented with FPGA. The total gate count is about 1 million with 530, 432-bit embedded memory cells and it operates at 15 MHz. The functionality and performance of the proposed processor is verified with simulation of oil reservoir problem using diffusion equations and character recognition application using ANNs. The execution times of two applications are compared with software realizations on 1.7 GHz Pentium IV personal computer. Though the proposed processor architecture and the instruction set are optimized for diffusion equations and ANNs, it provides flexibility to program for many other scientific computation algorithms.