The phase angle of a fractional-order capacitor's (FOC) impedance has a constant value between −90° and 0°. Maintaining this value over a broad frequency band is of utmost importance since it increases the applicability of the electrical circuit that employs the fractional-order capacitor (FOC). In this work, a molybdenum disulfide (MoS2)-ferroelectric polymer composite is used to design/fabricate an FOC. The resulting FOC's bandwidth of operation, which is defined as the frequency band where the variation in the phase angle is no more than ±4°, is five decades between 100 Hz and 10 MHz, a 3 decades improvement over the best reported state of the art. The value of the constant phase angle can be tuned from −80° to −58° by changing the type of the ferroelectric polymer in the composite and the volume ratio of MoS2. The results presented in this work demonstrate the potential of the FOCs fabricated using MoS2-ferroelectric polymer composites in robust and accurate realization of various electrical systems.