We report on the development of a 2.74-mJ, ~4.2 ps, ~258 nm deep-ultraviolet (DUV) source at 1 kHz based on frequency quadrupling of ~32 mJ, 8.4 ps, ~1030 nm near-infrared (NIR) laser pulses with an excellent beam profile, generated from a diode-pumped, ultrafast hybrid Yb-doped chirped-pulse amplification laser system. We have used a two-stage second harmonic generation scheme at LBO (NIR-to-green) and BBO crystals (green-to-DUV), respectively, to achieve the fourth-harmonic generation (FHG). The NIR-to-DUV conversion efficiency of ~10% in the FHG is obtained. The peak power of the produced DUV laser pulses is as high as 0.56 GW. The beam profiles at near-field and far-field are found to be excellent and the M2 value is measured as ~2.6. We also present the systematic parameter study on the optimization of DUV generation. To our best knowledge, this is the most energetic DUV generation from a diodepumped solid-state laser at kHz repetition rates.