The high spatial resolution observation of a quiet region taken with the Solar Optical Telescope/Spectro-Polarimeter aboard the Hinode spacecraft is analyzed. Based on the Milne-Eddington atmospheric model, the vector magnetic field of the quiet region is derived by fitting the full Stokes profiles of the Fe i 630 nm line pair. We extract intranetwork (IN) region from the quiet region and identify 5058 IN magnetic elements, and study their magnetic properties. As a comparison, the magnetic properties of network (NT) region are also analyzed. The main results are as follows. i) The IN area displays a predominance of weak (hecto-gauss) field concentration, i.e., 99.8 % of IN area shows the weak field. Moreover, the vector magnetic field exhibits concentration toward horizontal direction. However, for the NT region, we discover the coexistence of weak field and strong (kilo-gauss, kG) field. In the IN and NT regions, the filling factor shows almost the same probability distribution function with the peak at about 0.28. ii) All IN magnetic elements show field strength less than 1 kG. However, some NT elements display the coexistence of weak field and strong field. Regardless of NT or IN elements, about 20 % of elements lies in the Doppler blue-shift region. Our results imply that not all magnetic elements lie in the down-draft sites.