A new brace type damper was proposed in this paper, which was designed for protecting structures from earthquakes. The new brace type damper consists of two slit dampers and one H–type brace. The slit damper comprises a few perforated webs and two flanges, and the earthquake energy are dissipated through flexural yielding of perforated webs under in–plane shear. Compared with popular buckling restrained brace (BRB), the perforated web H–type brace damper (PWHBD) has some advantages of much cheaper, easier replacement, and more convenient detection. A quasi–static test was performed to investigate the hysteretic performance of three PWHBDs under cyclic loading. The influences of number of perforated webs and length versus width ratio of strips on the seismic behavior of PWHBD were analyzed. The failure modes, load–displacement curves, skeleton curves, stiffness, ductilities, energy dissipation, and strain were studied. The experimental results indicated that the hysteretic curves of PWHBDs were full, and the displacements corresponding to ultimate capacities of PWHBDs were above 18 mm, corresponding to more than 2.0% inter–storey drift. After then, a finite element model of PWHBD was developed through ABAQUS finite element software. The finite element model was verified through experimental results. The influences of length and width of strip, thickness of perforated web, and number of perforated webs on the seismic performance of PWHBD were further investigated. In addition, two existing formulas for slit damper were modified to calculate the initial stiffness and the yield capacities of PWHBDs, and then they were verified through experimental and numerical results.