A 13-T test facility with a 700-mm cold bore is being prepared for the research of high-field and high-current superconductors. Considering reuse of the existing cryostat, we select a pool-cooled and closely wound coil for the background field magnet to attain a large bore with the restricted outer diameter. The magnet is divided into two in the longitudinal direction and six in the radial direction. Rectangular monolithic conductors of Nb 3 Sn and NbTi are selected for the inner six coils and the outer six coils, respectively. To reduce the highest voltage of the Nb 3 Sn coil below 1.5 kV, the protection circuit of the Nb 3 Sn coils is separated by a circuit breaker from that of the NbTi coils. In addition, the half of protection resistors for the Nb 3 Sn coils is connected between the upper half and lower half of the Nb 3 Sn coils. The quench protection system consists of eleven 1-kV dc circuit breakers, ten protection resistors, and two diodes. According to the quench analyses with taking account of heat transfer between layers and the effect of resistance of a propagating normal zone on the current, the highest temperature is considerably lower than the adiabatic hotspot temperatures.