We present the design of an extreme ultraviolet (XUV) pulse shaper relying on reflective optics. The instrument will allow tailoring of the time-frequency spectrum of femtosecond pulses generated by seeded free-electron lasers (FEL) and high-harmonic generation (HHG) sources down to a central wavelength of ~15 nm. The device is based on the geometry of a 4f grating compressor that is a standard concept in ultrafast laser science and technology. We apply it to shorter wavelengths using grazing-incidence optics operated under ultra-high vacuum conditions. The design blaze angle and the line density of the gratings allow the manipulation of all different harmonics typical for seeded FEL and HHG photon sources without the need of realignment of the instrument and even simultaneously in multi-color experiments. A proof-of-principle pulse shaping experiment using 266 nm laser light has been performed, demonstrating relative phase-control of femtosecond UV pulses.