The distribution and contents of conductive fillers have a decisive influence on the dielectric properties of polymer/conductive filler composites. Herein, we clarified how the phase morphology and filler contents affect the dielectric properties of poly(ether ether ketone) (PEEK)/polyimide (TPI)/multi-walled carbon nanotubes (MWCNTs) composites, in which MWCNTs were selectively located in the TPI phase. Firstly, PEEK/TPI/MWCNTs composites with identical MWCNTs content but different PEEK/TPI ratios were prepared. The composites with co-continuous phase structure exhibited much better dielectric properties than those with sea-island structure. Then, PEEK/TPI/MWCNTs composites with the same PEEK/TPI ratio but various MWCNTs contents were prepared. The dielectric constant of the composite with 2 wt% MWCNTs reached 11306, which is because the formation of a co-continuous phase structure benefited the mini-capacitor network. Our results provide an effective method to develop high-dielectric-constant composites using the concept of double percolation.