The sandwich-structured Al2O3/low density polyethylene (Al2O3/LDPE) nanocomposite dielectrics consisting of layer-by-layer with different concentration Al2O3 loading were prepared by melt-blending and following hot pressing method. The space charge distribution from pulsed electro-acoustic method and breakdown strength of the nanocomposites were investigated. Compared with the single-layer Al2O3/LDPE nanocomposites, the sandwich-structured nanocomposites remarkably suppressed the space charge accumulation and presented higher breakdown strength. The charges in the sandwich-structured nanocomposites decayed much faster than that in the single-layer nanocomposites, which was attributed to an effective electric field caused by the formation of the interfacial space charges. The energy depth of shallow and deep traps was estimated as 0.73 eV and 1.17 eV in the sandwich-structured nanocomposites, respectively, according to the thermal excitation theoretical model we proposed. This work provides an attractive strategy of design and fabrication of polymer nanocomposites with excellent space charge suppression.