We investigate low-lying bound states of the neutron-rich nucleus B-15 by assuming it is a three-body system made of an inert core B-13 and two valence neutrons. The three-body wave functions are obtained using the Faddeev formalism. Special attention is paid to the excited state at 3.48(6) MeV observed in the (13)c(14c,N-12)B-15 reaction, whose properties are less clear theoretically. In our three-body model, besides the ground state 3/(2)2 a second 3/(2)2- state is discovered at around 3.61 MeV, which might be identified with the excited state observed at 3.48(6) MeV. We study this 3/(2)2- state in detail. It turns out to be a two-neutron halo state with a large matter radius r(m)approximate to 4.770 fm.