A positive-negative tunable liquid crystal lens array is proposed by electrode design. The electrode structure consists of two main units, one of them is used to generate parabolic voltage profile and the other one distributes the voltage homogeneously across the lens aperture. The proposal features the advantages of high-quality performance, simple fabrication process (a single lithographic step), compact design, low voltages and simple driving method. In addition, the lens array can be driven as a square lens array or a rotatable cylindrical lens array. The voltage difference between the electrodes on the inner face of two substrates is controlled within the range that the phase of liquid crystal layer responds linearly to voltage difference, then the phase of the lens array maintains parabolic profile in the whole focus range. In experiments, a lens array with 30 µm liquid crystal layer is fabricated using the designed electrode. The size of the array area is 11 × 11 mm, and the side length of an individual square lens is 1.0 mm. The results show that the phase profile matches with the parabolic profile during focus tuning, and good focusing effect of the positive lens is observed. As a result, a liquid crystal lens array with high-quality performance is experimentally demonstrated, and the experimental results are consistent with the theoretical analyses.