This work aims to investigate a new polymeric compound based on polymethyl methacrylate (PMMA) combined with micro and nano particles of zirconium oxide for medical and nonmedical radiation protection applications. To design a suitable shield against neutrons, PMMA was filled with 15, 30, and 45 wt% of ZrO2 micro and nano particles. The shielding properties of the proposed polymer mixtures were evaluated using a 252Cf neutron source. A neutron/gamma spectrometer with an organic scintillation stilbene detector (4 × 4 cm) was used to count the transmitted spectra of fast neutrons passing through the investigated polymer composites. The results showed that the studied compounds containing ZrO2 particles, for both the micro- and nano-particle sizes, showed reasonable neutron shielding properties compared with other conventional materials. In addition, the results illustrated that generally the nano particle was more effective than the same percentage of the additive micro particle at fixed neutron energy and ZrO2 wt%. Moreover, the highest relative improved percentages in macroscopic removal cross-section (MRCS) values between nano- and micro-particle composites were 7.37%, 5.28%, and 3.89% achieved for the investigated composites coded as P_15nZr, P_30nZr, and P_45 nZr samples, respectively. The total macroscopic value of thermal neutrons was calculated using neutron activation and a scattering calculator (ncnr.nist.gov). Moreover, fast neutron removal cross sections at 4.5 MeV and MRCS across a wide energy range of fast neutrons transmitted through the investigated compositions were calculated using Phy-X/PSD and MRCScal software, respectively. Good agreement between the calculated and the measured MRCSs was observed with maximum relative deviation not exceeding 6.211%. The obtained results show that the P_15nZr composition with nano particles of 15 wt% of ZrO2 had the highest MRCS value (0.1356 cm−1).