The 3MW TRIGA Mark-II Research Reactor of Bangladesh Atomic Energy Commission (BAEC) has been under operation for about thirty years since its commissioning at 1986. In accordance with the demand of fundamental nuclear research works, the reactor has to operate at different power levels by utilizing a number of experimental facilities. Regarding the enquiry for safety of reactor operating personnel and radiation workers, it is necessary to know the radiation level at different strategic points of the reactor where they are often worked. In the present study, neutron, beta and gamma radiation dose rate at different strategic points of the reactor facility with reactor power level of 2.4MW was measured to estimate the rising level of radiation due to its operational activities. From the obtained results high radiation dose is observed at the measurement position of the piercing beam port which is caused by neutron leakage and accordingly, dose rate at the stated position with different reactor power levels was measured. This study also deals with the gamma dose rate measurements at a fixed position of the reactor pool top surface for different reactor power levels under both Natural Convection Cooling Mode (NCCM) and Forced Convection Cooling Mode (FCCM). Results show that, radiation dose rate is higher for NCCM in compared with FCCM and increasing with the increase of reactor power. Thus, concerning the radiological safety issues for working personnel and the general public, the radiation dose level monitoring and the experimental analysis performed within this paper is so much effective and the result of this work can be utilized for base line data and code verification of the nuclear reactor.