We present the development and implementation of a spatially and spectrally resolved multipoint fluorescence correlation spectroscopy (FCS) system utilizing multiple end-capped optical fibers and an inexpensive laser source. Specially prepared end-capped optical fibers placed in an image plane were used to both collect fluorescence signals from the sample and to deliver signals to the detectors. The placement of independently selected optical fibers on the image plane was done by monitoring the end-capped fiber tips at the focus using a CCD, and fluorescence from specific positions of a sample were collected by an end-capped fiber, which could accurately represent light intensities or spectral data without incurring any disturbance. A fast multipoint spectroscopy system with a time resolution of $\sim 1.5\mathrm{ms}$ was then implemented using a prism and an electron multiplying charge coupled device with a pixel binning for the region of interest. The accuracy of our proposed system was subsequently confirmed by experimental results, based on an FCS analysis of microspheres in distilled water. We expect that the proposed multipoint site-specific fluorescence measurement system can be used as an inexpensive fluorescence measurement tool to study many intracellular and molecular dynamics in cell biology.