Body-centered tetragonal C4 (bct C4) is a new form of crystalline sp(3) carbon, which is found to be transparent,dynamically stable at zero pressure and more stable than graphite beyond 18.6 GPa. Symmetry analysis of the vibrational modes of bct C4 at Brillouin zone center is performed, Raman and infrared active modes are identified. The analysis results show that, different from cubic diamond and hexagonal diamond, there is an infrared active mode in bct C4. Based on first-principle method within the local density approximation, vibrational frequencies, Born effective charge tensors, and infrared absorption intensity of bct C4 are obtained. The vibrational modes of bct C4 are presented and compared with those of cubic diamond and hexagonal diamond in detail.