Aiming at the problem that the stress concentration at the sharp corners of lattice strut joints in conventional BCC lattice structures can lead to yield, this paper presents a design method of filleted BCC lattice structure (BCC-F) to reduce the stress concentration and ensure the structural safety for lattice structure. Validation was conducted through numerical simulation based on homogenization method and uniaxial compression tests on three groups of Ti–6Al–4V BCC and BCC-F lattice specimens. The results show that the filleted lattice joint can realize the geometrically smooth transition at the intersection of the lattice struts, and significantly improve the effective Young’s modulus and effective yield stress of the low-density BCC lattice structure, and change the failure mode of lattice structure. When the relative density of BCC and BCC-F were 0.327 and 0.370, the increase of effective Young’s modulus and effective yield stress of BCC-F were 142% and 64%, respectively, and the failure mode of BCC-F presented the characteristics of “multi-wave peak” collapse.