Based on the technique of fragment-induced spin polarization combined with the β-NMR method, we have recently carried out experiments at RIKEN to measure nuclear moments of neutron-rich aluminum isotopes. In the measurements, the nuclear magnetic-dipole moments of 30, 32Al and the electric-quadrupole moments of 31,32Al have been determined. The obtained magnetic moments, as well as the other known magnetic moments of aluminum isotopes, agree well with shell model calculations with the USD interaction. The obtained quadrupole moments are smaller than those of 27, 28Al, suggesting spherical shapes of 31, 32Al. These results seem to suggest that 31Al and 32Al are located outside the island of inversion. In near future, studies on nuclear moments will be extended further in the RIKEN RIBF project, in which medium- and heavy-mass regions come within our scope by using superconducting fragment separator BigRIPS. Also, an upgrade program for the existing fragment separator RIPS is in progress. In the RIBF project, nuclear moments will be measured for isomer states as well as ground states.