The continuous carbon fiber reinforced Polyether-ether-ketone (PEEK) prepreg tapes with the addition of carbon nanotubes (CNTs) were prepared by a wet powder impregnation process. Their electrical conductivity, thermal conductivity, the tensile properties, dynamic mechanical behavior, fracture morphology and crystallization melting behavior were investigated. The results show that, the electrical conductivity (σ), thermal conductivity (λ), tensile strength (σ t) and interfacial adhesion of the prepreg tapes were obviously improved with the addition of CNTs. When CNT content was 1.0 wt%, the σ of CNT/CCF/PEEK prepreg tapes in the 0° direction reached a maximum value of 0.701 s cm−1, which was increased 165% than that of CCF/PEEK prepreg tapes. The λ reached 1.053 W m−1·K−1, which was improved by 12.14%. The tensile strength was 1489 MPa, which was increased by 16.4%. The results of SEM images show that the interface adhesion between the fiber and the matrix is good. The results of DMA indicate that, the capability of deformation resistance of the prepreg tapes were further improved with the addition of CNTs. When the temperature was 280 °C, the decline rate of E′ of 1.0 wt% CNT/CCF/PEEK prepreg tapes were 3.58%. The results of DSC indicate that, the T c of CNT/CCF/PEEK prepreg tapes moved to high temperature after adding CNTs, which indicate that CNTs played a role of heterogeneous nucleation in the PEEK matrix.