To perform basic research and development to realize future accelerator-driven systems, a lead-bismuth eutectic (LBE) alloy spallation target will be installed within the framework of the Japan Proton Accelerator Research Complex (J-PARC) project, Japan Atomic Energy Agency. The target will be bombarded by high-power pulsed proton beams (250 kW, 400 MeV, 25 Hz, and 0.5 ms in pulse duration). The beam window (BW) of the spallation target is critical because it should survive under severe conditions that occur, i.e., high temperature, high irradiation, intense stress, and various kinds of damage. Therefore, the target vessel should be carefully designed to obtain an adequate safety margin. Our previous research indicates that there is a stagnant flow region in the LBE at the BW tip due to the symmetric configuration of the target, which causes high temperature and concentration of stress on the BW. On the basis of our previous work, three types of upgraded target head designs are studied in the current research to reduce/move the stagnant flow region from the BW tip and to increase the target safety margin. Thermal-hydraulic analyses and structural analyses for the target head designs are carried out numerically under a steady-state condition. Results illustrate that the designs can almost eliminate the stagnant flow region in the LBE. As a consequence, the concentration of thermal stress on the BW is released and greatly decreased. The safety margin of the target is improved through this study.