THz (terahertz) properties of MgF2 crystal (sample 1) and MgF2: Co crystal (sample 2) is measured using transmission THz time domain spectroscopy in the frequency range between 0.5 and 2.5 THz. The absorption coefficients α(ν) of sample 1 increases and has a maximum 24cm-1 with increasing frequency ν from 0.5　THz to 2.5　THz. The absorption coefficient of sample 2 is much larger than that of the sample 1, and its absorption band edge of the crystal lattice shifts to lower frequency side because of the dopant Co. Moreover, there is an absorption peak at 1.9THz and the absorption coefficient is greater than 70 cm-1, the force constant K of F-—Co2+ ionic chemical bond stretch vibration calculated from this peak is 3.40×10-2　N/cm. The THz spectroscopy can be an important technique for research of chemical bond in crystal. Real dielectric functions between 0.5 and 2.5 THz of the two samples are calculated by relations between optical constants. The ε1(ν) of sample 1 varies from 4.67 to 4.73 and ε1(ν) of sample 2 varies from 4.62 to 5.01.