Lattice structures are characterized by a light weight, high strength, and high stiffness, and have a wide range of applications in the aerospace field. Node stress concentration is a key factor affecting the mechanical performance of lattice structures. In this paper, a new equal-strength body-centered cubic (ES-BCC) lattice structure was additively manufactured using 316L stainless steel via selective laser melting (SLM). The results of a mechanical compression test and finite element analysis revealed that the failure location of the ES-BCC structure changed from the nodes to the center of the struts. At the same density, the energy absorption, elastic modulus, and yield strength of the ES-BCC structure increased by 11.89%, 61.80%, and 53.72% compared to the BCC structure, respectively. Furthermore, the change in angle of the ES-BCC structure achieves significant changes in strength, stiffness, and energy absorption to meet different design requirements and engineering applications. The equal-strength concept design can be applied as a general design method to the design of other lightweight energy-absorbing lattice structures.