Electromagnetically induced transparency (EIT) and slowing-down of group velocity (SGV) in Eu3+∶Y2SiO5 were investigated by using the density matrix equations of the interaction between the light and the matter and their numerical solutions. The relationship of the probe transmissivity with different probe detuning and coupling Rabi frequency was obtained. The influence of inhomogeneous line width on electromagnetically induced transparency and slowing-down of group velocity were analyzed. Electromagnetically induced transparency was restrained when increasing the inhomogeneous line width. The center transmission was not homogeneously change with the increase of ions-doped concentration. There is an optimal concentration which can make the electromagnetically induced transparent remarkable. It is evident that group velocity of the probe has a minimum value for a certain coupling field strength.