HD$^+$ hydrogen molecular ion is of metrological interest due to possibility of precise theoretical evaluation of its spectrum and of external-field-induced shifts. In present work, the rates of laser-induced electric quadrupole transitions are calculated for a wide range of rovibrational transitionsin particular for L0-L’2, L1-L’3, L2-L’4 (v=(0-10)-v’=(0-3)). Results are presented with six significant digits.