The present application relates to new and distinct cultivar of primocane-fruiting raspberry named ‘PBBrasp1348’. The new variety reliably provides balanced heavy crop load on both primocanes and floricanes, with large, glossy, non-darkening, broad-conic fruits of medium adherence to the receptacle. Plants possess high vigor, produce high numbers of spawn, and branch naturally along the main cane. Susceptibility to yellow rust (Phragmidium rubi-idaei) has been observed. Field tolerance to Raspberry Bushy Dwarf Virus (RBDV) and Phytophthora root rot has been observed.