Low-density polyethylene (LDPE) based nanocomposites are capable of suppressing the accumulation of space charges and enhancing the resistivity and electrical breakdown strength, which are beneficial for the performance and reliability of high voltage direct current power cables. Incorporating nanofillers into polymers can form interfacial regions inside and affect both the trap distribution and molecular motion characteristics, resulting in changes in the dielectric properties of polymer nanocomposites. To unravel the influencing mechanism of interfacial traps and molecular motion on the dc electrical breakdown strength, we investigate the dc electrical breakdown properties of LDPE/Al2O3 nanocomposites as a function of nanofiller loading, pressure, ramping rate of voltage, and sample thickness by experiments and simulations of the charge transport and molecular displacement modulated electrical breakdown. Experimental and simulation results are consistent and show that dc electrical breakdown strength increases firstly and then decreases with the increase of nanofiller loading, increases monotonically with increasing pressure and ramping rate of voltage, and decreases with the increase in sample thickness, obeying an inverse power law. It is indicated that the dc electrical breakdown of LDPE/Al2O3 nanocomposites is triggered by the local current and energy multiplication caused by charge carriers jumping over deep traps when they gain sufficient energy in the enlarged free volume via molecular displacement. It is concluded that both the increase in deep trap energy and the restraint of the motion dynamics of molecular chains with occupied deep traps can enhance the dc electrical breakdown strength of LDPE/Al2O3 nanocomposites.