The Multi-Object Optical and Near-infrared Spectrograph (MOONS) is a new fiber-fed spectrograph for the VLT. MOONS will exploit the full 500 square arcmin field of view offered by the Nasmyth focus of VLT and will be equipped with two dual-arm spectrographs covering the wavelength range 0.8 mu m-1.8 mu m, with a possible extension down to 0.5 mu m. Each double-arm spectrograph will produce spectra for 250 targets simultaneously, each with its own dedicated sky fiber for optimal sky subtraction. The system will have both a medium resolution (R 3000 - 5000) mode and a high resolution (R 20000) mode to allow detailed dynamical and chemical studies. To ensure the accurate positioning of the 500 fiber pairs over the focal plane that has 880 mm in diameter, a metrology system has been designed to provide position measurements within 7.5 mu m considering that the final positioning accuracy of each fiber with respect to the target object must be less than 15 mu m. The metrology system is composed by a circular array of 12 cameras located at VLT's de-rotator ring around the Nasmyth focus. The paper presents the design of the metrology system and discusses the proposed methodology to align multiple the views of the focal plane array.