A type of all-polymer percolative composite is introduced which exhibits a very high dielectric constant (> 7000). The experimental results also show that the dielectric behavior of this new class of percolative composites follows the predictions of the percolation theory and the analysis of conductive percolation phenomena. The very high dielectric constant of the all-polymer composites, which are also very flexible and possesses an elastic modulus close to that of the insulation polymer matrix, makes it possible to induce a high electromechanical response under a very reduced electric field (a strain of 2.65% with an elastic energy density of 0.18 J cm(-3) can be achieved under a field of 16 MV m(-1)). Data analysis also suggests that within the composites, the non-uniform local field distribution as well as interface effects can significantly enhance the strain responses. Furthermore, the experimental data as well as the data analysis indicate that conduction loss in the composites will not affect the strain hysteresis.