The X-ray spectrometer used in high-energy-density plasma experiments generally requires both broad X-ray energy coverage and high temporal, spatial, and spectral resolutions for overcoming the difficulties imposed by the X-ray background, debris, and mechanical shocks. By using an elliptical crystal together with a streak camera, we resolve this issue at the SG-II laser facility. The carefully designed elliptical crystal has a broad spectral coverage with high resolution, strong rejection of the diffuse and/or fluorescent background radiation, and negligible source broadening for extended sources. The spectra that are Bragg reflected (23°<θ<38°) from the crystal are focused onto a streak camera slit 18 mm long and about 80 μm wide, to obtain a time-resolved spectrum. With experimental measurements, we demonstrate that the quartz(1011) elliptical analyzer at the SG-II laser facility has a single-shot spectral range of (4.64–6.45) keV, a typical spectral resolution of E/DE = 560, and an enhanced focusing power in the spectral dimension. For titanium (Ti) data, the lines of interest show a distribution as a function of time and the temporal variations of the He-a and Li-like Ti satellite lines and their spatial profiles show intensity peak red shifts. The spectrometer sensitivity is illustrated with a temporal resolution of better than 25 ps, which satisfies the near-term requirements of high-energy-density physics experiments.