This paper proposes new processor architecture for accelerating data-parallel applications based on the combination of VLIW and vector processing paradigms. It uses VLIW architecture for processing multiple independent scalar instructions concurrently on parallel execution units. Data parallelism is expressed by vector ISA and processed on the same parallel execution units of the VLIW architecture. The proposed processor, which is called VecLIW, has unified register file of 64x32-bit registers in the decode stage for storing scalar/vector data. VecLIW can issue up to four scalar/vector operations in each cycle for parallel processing a set of operands and producing up to four results. However, it cannot issue more than one memory operation at a time, which loads/stores 128-bit scalar/vector data from/to data cache. Four 32-bit results can be written back into VecLIW register file. The complete design of our proposed VecLIW processor is implemented using Verilog HDL.