Plenoptic cameras are a new type of sensor that extend the possibilities of current commercial cameras allowing 3D refocusing or the capture of 3D depths. One of the limitations of plenoptic cameras is their limited spatial resolution. In this paper we describe a fast, specialized hardware implementation of a super-resolution algorithm for plenoptic cameras. The algorithm has been designed for field programmable graphic array (FPGA) devices using VHDL (very high speed integrated circuit (VHSIC) hardware description language). With this technology, we obtain an acceleration of several orders of magnitude using its extremely high-performance signal processing capability through parallelism and pipeline architecture. The system has been developed using generics of the VHDL language. This allows a very versatile and parameterizable system. The system user can easily modify parameters such as data width, number of microlenses of the plenoptic camera, their size and shape, and the super-resolution factor. The speed of the algorithm in FPGA has been successfully compared with the execution using a conventional computer for several image sizes and different 3D refocusing planes.