In this paper, a new type of buckling‐restrained brace characterized by a variable cross‐section core (BRB‐VCC) is proposed and investigated. The practical design equations of the BRB‐VCC are derived based on mechanical and mathematical theories. Six specimens are designed and tested to clarify the mechanical behaviours of the BRB‐VCC and to validate the reliability of the proposed equations. The test results show that (1) none of the specimens buckle under compression, as expected, and their ductilities and energy dissipation capacities are satisfactory; (2) the derived formulas are reliable and can be conveniently used in engineering practice; and (3) the yielding displacement of the BRB‐VCC is approximately 70% that of the traditional TJ‐1 buckling‐restrained brace (BRB‐TJ‐1), which may yield earlier than the BRB‐TJ‐1 in concrete structures under the action of an earthquake.