Filter capacitors play a critical role in ensuring the quality and reliability of electrical and electronic equipment. Aluminum electrolytic capacitors are the most commonly used but are the largest filtering components, limiting device miniaturization. The high areal and volumetric capacitance of electric double-layer capacitors should make them ideal miniaturized filter capacitors, but they are hindered by their slow frequency responses. We report the development of interconnected and structurally integrated carbon tube grid-based electric double-layer capacitors with high areal capacitance and rapid frequency response. These capacitors exhibit excellent line filtering of 120-hertz voltage signal and volumetric advantages under low-voltage operations for digital circuits, portable electronics, and electrical appliances. These findings provide a sound technological basis for developing electric double-layer capacitors for miniaturizing filter and power devices.