This study proposes a three-channel (3-channel) variable filter-bank (VFB) that consists of variable lowpass, variable bandpass and variable highpass digital filters. The three variable digital filters are obtained from a normalised analog prototype Chebyshev type-I lowpass filter using analog frequency transformations along with a modified bilinear transformation. Since both the magnitudes (gains) and band edge frequencies of the three variable digital filters are independently adjustable, the 3-channel VFB is considerably flexible, and can be successfully applied for compensating various hearing loss patterns in digital hearing aids. Various audiograms have been used to verify that high-accuracy fittings can be achieved with low order variable filters. Moreover, the authors reveal and theoretically prove the numerator coefficient-symmetries of the variable lowpass, variable bandpass and variable highpass filters, and show that each variable filter requires only one multiplication for its numerator filtering operations, so the total number of multiplications can be significantly reduced. More specifically, only 11 multiplications and 14 additions are required in the whole 3-channel VFB. Therefore the 3-channel VFB has extremely simple structure and high tuning flexibility for hearing aids.