We have investigated the elastic constants of the ternary rare earth compound HoB2C2 with a tetragonal structure, by means of the ultrasonic method. The elastic constants of (C-11- C-12)/2, C-44 and C-66,, corresponding to the transverse ultrasonic modes exhibit the softening proportional to reciprocal temperature below about 40 K. This softening is commonly enhanced in the ordered phase IV below T-C1 = 5.9 K. An abrupt increase of elastic constants is found in the ordered phase UI below T-C2 = 5,0 K characterized by the simultaneous antiferro-type ordering of electric quadrupole and magnetic dipole moments. The quadrupole susceptibility based on a model consisting of a ground state E-doublet and an excited singlet with a low energy in HoB2C2 is employed for the analysis of the softening above T-C1 = 5.9 K. The enhancement of the elastic softening in the phase IV of HoB2C2 resembles to the soft C44 mode in the phase IV in Ce0,751La0.25B6.