This article reports on the fabrication of modified high-density polyethylene (HDPE) foams with complex cellular structure (CCS) using supercritical CO2 as a physical blowing agent by a cooling and two-step depressurization method. HDPE was modified by dicumyl peroxide (DCP) and carbon nanotubes (CNTs) to improve its viscoelasticity and foaming behavior. The gel content test demonstrated that the cross-liriking structure formed in the modified HDPE samples. Compared with that of neat HDPE, the viscoelasticity of modified HDPE was improved largely, which was characterized by rotational rheometer and torque rheometer. The introduction of DCP and CNTs had a slightly effect on the thermal behaviors of HDPE. The foaming properties of various HDPE samples showed that the cross-linking structure caused by DCP improved the foamability of HDPE and CNTs acted as a nucleating agent for cell nucleation. The degree of the first-step depressurization was critical to control the CCS evolution in HDPE foam. (C) 2017 Elsevier B.V. All rights reserved.