The neutron flux of the Triga Mark III research reactor was studied using nuclear track detectors. The facility of the National Institute for Nuclear Research (ININ), operates with a new core load of 85 LEU 30/20 (Low Enriched Uranium) fuel elements. The reactor provides a neutron flux around 2 × 1012 n cm-2s-1 at the irradiation channel. In this channel, CR-39 (allyl diglycol policarbonate) Landauer® detectors were exposed to neutrons; the detectors were covered with a 3 mm acrylic sheet for (n, p) reaction. Results show a linear response between the reactor power in the range 0.1 - 7 kW, and the average nuclear track density with data reproducibility and relatively low uncertainty (±5%). The method is a simple technique, fast and reliable procedure to monitor the research reactor operating power levels.