For traditional capacitive pressure sensors, high nonlinearity and poor sensitivity greatly limited their sensing applications. Hence, an innovative design of capacitors based on spiral comb electrodes is proposed for high-sensitivity pressure detection in this work. Compared to traditional capacitive pressure sensors with straight plate comb electrodes, the proposed sensor with the spiral comb electrodes increases the overlap areas of electrodes sufficiently, the pressure sensitivity can thus be greatly improved. Moreover, the capacitance variation of the proposed sensor is dominated by the change of the overlap area of the electrodes rather than the electrode’s distance, the linearity can also thus be improved to higher than 0.99. Theoretical analysis and COMSOL-based finite element simulation have been implemented for principle verification and performance optimization. Simulation results show that the proposed design has a mechanical sensitivity of 1.5 × 10−4 m Pa−1, capacitive sensitivity of 1.10 aF Pa−1, and nonlinear error of 3.63%, respectively, at the pressure range from 0 to 30 kPa. An equivalent experiment has been further carried out for verification. Experimental results also show that both the sensitivity and linearity of capacitive pressure sensors with spiral comb electrodes are higher than those with straight comb electrodes. This work not only provides a new avenue for capacitor design, but also can be applied to high-sensitivity pressure detection.