A (Nb, Ti)₃Sn superconductor with high critical current density (J_c) for a 1GHz NMR magnet has been developed on the base of a so-called bronze process by using a matrix of Cu-15 wt% Sn-0.3 wt% Ti. To investigate the effects of increase in tin content on J_c and n value, another conductor with a conventional matrix of Cu-13 wt% Sn-0.3 wt% Ti was fabricated for comparison. The developed conductor showed a distinct increase in J_c in comparison with the conventional one. Based on microscopic investigations, the obtained improvement in J_c was attributed to an increase in reacted layer thickness and a decrease in grain size. The dependence of high field J_c on heat treatment conditions was also examined in relation to flux pinning. It then turned out that the J_c of the developed (Nb, Ti)₃Sn conductor in high fields of over 20T depends on the upper critical field rather than on the microstructures of (Nb, Ti)₃Sn. The developed conductor showed a J_c of 102A/mm² and n values of about 40 at 1.8K and 21T, fulfilling all target values in the preliminary design of a 1GHz NMR magnet.