In this work the dependence of intrinsic efficiency of a NaI(Tl) detector of radius 3.82 cm and height 7.62 cm on source-detector distance (d), source-off-axis distance (d0) and γ-photon energy have been investigated using analytical and Monte Carlo methods. The results showed that, for a given off-axis distance, there exists a value of the ratio of source-detector distance (d) to detector radius (R) where intrinsic efficiency is minimum. This d/R value at which minimum efficiency occurs approaches zero as offaxis distance increases and it is almost constant with increase in energy. In the region where d/R < 0.01, a criteria given by Jehouani et al [1] for good photon detection, intrinsic efficiency decreases with increasing off-axis distance. The implications of the results for radioactivity measurement and radiation protection are discussed. Chacteristics of intrinsic efficiency in the regions d/R < 0.01 and d/R > 10 are also compared.