A gated multiple-sampling and tracking proportional chamber (GMSTPC) has been made for the study of ( α , n) and (p, n) type reactions of astrophysical interest induced by low-energy radioactive nuclear beam. It consists of a drift-space region, a proportional-counter region divided into 24 segments and a gating grid. The GMSTPC is placed in such a way that the beam enters directly into its drift space, so that the chamber gas also acts reaction targets. The gating grid allows the gas multiplication of electrons only when it is triggered by neutron signals. Under the operation of this gating grid, almost no pulse-height defects have been observed up to 40 kHz beam-injection rates. Characteristics and performance of the GMSTPC are reported. We also describe some details of a whole detector system including a time-of-flight counter, a neutron-counter wall consisting of 28 plastic-scintillator bars and the GMSTPC, with which three-dimensional trajectories and energies of both charged particles and neutrons can be measured event by event. The measured efficiency of the detector system as well as the analysis efficiency in the case of the Li 8 ( α , n ) reaction are also given.