We report ab initio relativistic 20-electron correlation calculations of electric-dipole transition moments for nine low-lying electronic states of HfF+, which it is suggested to be used in experiments to search for the electric-dipole moment of the electron. Radiative lifetimes for the lowest vibrational levels of the first excited (3)Delta(1) electronic state are calculated and its population scheme is suggested. The influence of correlation of the 4f electrons of Hf is studied.