To gain high dielectric constant, polymer composites with 1D fillers are researched for energy storage. However, high leakage conduction from polymer/filler interface and filler interconnection can induce high dielectric loss. For high dielectric constant and low dielectric loss, in this work, we raised a strategy of morphological synergy of fillers (1D catenulate semi-conductive CuO nano-filler and 0D insulating alumina nano-particles) to fabricate polymer-based ternary composites. Instead of 0D CuO, 1D CuO nano-chains with the improved specific surface area were employed for high dielectric constant via polymer/CuO interface polarization. Spherical alpha-alumina nano-particles were used for reducing polymer/CuO interface leakage conduction and depressing CuO percolation to gain low dielectric loss. Compared with rather high dielectric constant and dielectric loss in polymer/CuO binary composites, moderately high dielectric constant and rather low dielectric loss were achieved in ternary composites. Via excellent synergy of CuO and alumina, ternary composites showed more promising dielectric properties. Ternary composite with 9 wt% CuO and 3 wt% alumina exhibited a high dielectric constant of ~ 64 and low dielectric loss of ~ 0.16 at 20 Hz. This work might pave a road for large-scale preparation of high-performance composite dielectrics by morphological synergy of fillers.