Crystallographic, electric, magnetic and heat transition properties of $alpha$-Fe$_2$O$_3$ have been studied with a small addition of Eu impurities. Hematite($alpha$-Fe$_2$O$_3$) is a basic ferromagnetic material having rhombohedral structure, which is similar to perovskites structure. Eu is a rare earth element that has an electric configuration of 4f$^{7}$ 6s$^2$. X-ray diffraction pattern of Fe$_{1-x}$ Eu$_{x}$O$_3$ (x = 0.00, 0.04, 0.06) shows an increament of a value when the amount of Eu impurities increased. The VSM data show an increment of magnetization by increasing the amount of Eu impurity. The one with x=0.06 shows the largest increment of magnetic remanence. The magnetic remanence varied from 0.49$ imes$10$^{-3}$ emu/g to 0.62$ imes$10$^{-3}$ emu/g when Eu impurity is increased by 2 %. Coercivity is decreased as Eu impurity is increased. Resistances is reduced significantly by Eu impurity. There is a clear difference in temperature-dependent resistance depending on the amount of Eu impurities. Especially, there are cusps between 150 K to 175 K. It indicates the change of electronic quantum states inside the atoms by rare earth impurities in rhombohedral structure. Temperature-dependent heat capacity shows that the most effective amount of Eu impurities is 6 %. %.