The reaction cross section for the neutron-rich nucleus B-17 on a carbon target has been measured at an energy of 77 AMeV by a transmission method. A large enhancement of 17B reaction cross section at low energy was observed. The density distribution of 17B was deduced through the energy dependence of the reaction cross section together with high-energy data using a finite-range Glauber-model calculation under an optical-limit approximation. It is confirmed that the neutron-tail in the density distribution is necessary for 17B in order to reproduce the measured reaction cross sections. Based on the assumption of a core (B-15) plus valence two-neutron picture, the mixture of v(2s(1/2)) and V(1d(5/2)) was studied without treating the correlation between two neutrons.