We present a novel double-clad step-index few-mode fiber that operates as a five-sampled tunable true-time delay line. The unique feature of this design lies in its particular modal chromatic dispersion behavior, which varies in constant incremental steps among adjacent groups of modes. This property, which to the best of our knowledge has not been reported in any other few-mode fiber to date, is the key to tunable operation of radiofrequency signal processing functionalities implemented in few-mode fibers. The performance of the designed true-time delay line is theoretically evaluated for two different microwave photonics applications, namely tunable signal filtering and optical beamforming networks for phased array antennas. In the 35-nm optical wavelength tuning range of the C-band, the free spectral range of the microwave filter and the beam-pointing angle in the phased array antenna can be continuously tuned from 12.4 up to 57 GHz and 12.6° up to 90°, respectively.