We describe a broadband (12.5-30 nm) extreme ultraviolet (XUV) spectrograph, which is stigmatic throughout its operating range. The instrument employs a near-normal-incidence aperiodic Mo/Si multilayer mirror and a grazing-incidence plane varied line-space (VLS) grating. Strict stigmatism is fulfilled simultaneously at two wavelengths and the condition of practical stigmatism is fulfilled over two octaves in wavelength. The vertically space-resolved line spectra of multiple charge ions from laser plasma were recorded to demonstrate a spectral resolving power of 103 and a spatial resolution of ~26 μm, both figures corresponding to two detector pixels. The electron density was evaluated from the Stark broadening of the Balmer line Hβ (135 Å) of C VI in the plasma excited by 0.5 J, 8 ns, 1.06 μm pulses.