The Infrared and Raman spectra of RNA nucleobases in terahertz (THz) band (1~10 THz) were detected with Fourier transform infrared spectroscopy (FTIR) and Raman spectroscopy. The position of all the characteristic peaks and corresponding vibration modes of RNA nucleobase crystals were obtained with Guassian09 software and energy-based fragmentation approach under periodic boundary conditions (PBC-GEBF) method. The computational results were verified to be in accordance with experimental data, which indicated that the powder of RNA nucleobases is amorphous crystal structure. The infrared spectra demonstrated that adenine, guanine and cytosine all have 6 infrared active vibrational modes, while uracil only has 3. Comparing to experimental results, the position and intensity of the absorption peaks were nicely corroborated by the predicted spectrum, except that one weak vibrational frequency at 6.35 THz is missing and two peaks (4.83 and 5.39 THz) merge in the predicted spectrum of guanine; two peaks in 4.3 and 4.79 THz merge into a single one in the calculated spectrum of cytosine; the peaks of thymine in 3.32 and 3.82 THz merged. The computational results of Raman spectra were also verified to be in line with the experimental data. The position and intensity of the characteristics peaks were exactly simulated except that two peaks of guanine in 3.52 and 4.48 THz merged; two peaks in 7.26 and 8.03 THz merge and five peaks (3.57, 4.02, 4.49, 4.89, 5.98 THz) merge in the calculated spectrum of guanine. Through the analysis and identification of the characteristic peaks, it is indicated that the vibration modes of DNA nucleobases in 1~10 THz were derived from collective vibration of molecules in the lattice. The intermolecular hydrogen bond and the weak interaction force contribute greatly to the vibration modes. In addition, as the frequency increases to over 5.5 THz, the vibration modes will change from the atoms collective vibration to some atoms vibration. This research has important theoretical and practical reference value to reveal the effect of RNA nucleobases in the areas of RNA molecular structure constitution, biological macromolecules identification and terahertz spectra formation mechanism and biological inheritance.