Low dose -irradiation effects on Polymethylmethacrylate (PMMA) polymer are studied by means of positron annihilation lifetime spectroscopy. An empirical formula is suggested to relate the ortho-positronium (o-Ps) lifetime,3 with the molecular weight of the polymer, Mn, and the concentration of the free radicals, [X], generated in PMMA polymer due to irradiation in air. It is shown that free radicals concentration increase with the absorbed dose, and it is measurable from the results of 3. The results showed that the positron lifetime parameters illustrate a significant behavior as the dose increase. In addition, a unique behaviors of the free positron annihilation parameters, 2 and I2, are reported. 2 is found to increase as the dose increased and the formation of (free radicals-positron) compound is thought to explain this result. The value of I2 is found to reach a nearly constant (saturated) value at a threshold dose, which is shown to support the lifetime results.