This study reports a novel approach to the implementation of 3D carbon nanotube (CNT) interdigitated finger electrodes on flexible polymer, and the detection of strain, bending curvature, tactile force and proximity distance are demonstrated. The merits of the presented CNT-based flexible sensor are as follows: (1) the silicon substrate is patterned to enable the formation of 3D vertically aligned CNTs on the substrate surface; (2) polymer molding on the silicon substrate with 3D CNTs is further employed to transfer the 3D CNTs to the flexible polymer substrate; (3) the CNT-polymer composite (~70 μm in height) is employed to form interdigitated finger electrodes to increase the sensing area and initial capacitance; (4) other structures such as electrical routings, resistors and mechanical supporters are also available using the CNT-polymer composite. The preliminary fabrication results demonstrate a flexible capacitive sensor with 50 μm high CNT interdigitated electrodes on a poly-dimethylsiloxane substrate. The tests show that the typical capacitance change is several dozens of fF and the gauge factor is in the range of 3.44-4.88 for strain and bending curvature measurement; the sensitivity of the tactile sensor is 1.11% N(-1); a proximity distance near 2 mm away from the sensor can be detected.