This work focuses on the coupling effect of molecular chain displacement and trap characteristics on direct current (DC) breakdown properties of high density/low density polyethylene (HDPE/LDPE) blend insulation. Frequency domain spectroscopy (FDS) and isothermal discharge current (IDC) are used to characterize the dielectric relaxation and trap characteristics of HDPE/LDPE blends. A DC breakdown model is proposed to reveal the mechanisms of the molecular chain displacement and carrier trap on the DC breakdown strength. The dielectric relaxation α and δ present segmental motions and thermal ion polarization behaviours of HDPE/LDPE blends, respectively. α dielectric relaxation strength (Δε_α) increases as the amount of HDPE increases from 0 to 5 wt%, and then declines with a further increase of HDPE content to 20 wt%. According to the velocity equation, the increase of Δεα will increase the molecular chain displacement, resulting in a larger free volume, which will provide electrons with larger free path λ to form hot electrons. A positive correlation exists between the activation energy of the dielectric relaxation process δ and trap density, and the increase of δ dielectric relaxation strength (Δε_δ) will adversely affect the breakdown strength of the specimen. HDPE/LDPE blends with 15 wt% HDPE content have lower Δε_α and lowest Δε_δ, which decreases the mean free path λ of molecular chain and thermal ion polarization. At the same time, it has the highest deep trap density, thus increasing the probability of hot electrons being captured and improving the DC breakdown strength. It is concluded the breakdown of the dielectric is synergistically affected by the molecular chain displacement and carrier trap.