The dihydrogen bonds B–H???H–X (X=F, Cl, Br, C, O, N) in the dimer (NH3BH3)2 and the complexes of NH3BH3 with HF, HCl, HBr, H2CO, H2O, and CH3OH were theoretically studied. The results show that formation of the dihydrogen bond leads to elongation and stretch frequency red shift of the BH and XH bonds, except that in the H2CO system, the CH bond blue shifts. For (NH3BH3)2 and the complexes of the halogenides, red shifts of the XH bonds are caused by the intermolecular hyperconjugation σ(BH)→σ*(XH). For the system of H2CO, a blue shift of the CH bond is caused by a decrease of the intramolecular hyperconjugation n(O) →σ¤(CH). In the other two systems, the red shift of OH bond is a secondary effect of the stronger traditional red-shifted H-bonds N–H???O. In all these systems, red shifts of the BH bonds are caused by two factors: negative repolarization and negative rehybridization of the BH bond, and decrease of occupancy on σ(BH) caused by the intermolecular hyperconjugation σ(BH)→σ¤(XH).