Using photon sieves as the spectral components, this paper designs a new soft X-ray spectrograph, and analyses its principles, structure and design. The theoretical measurement range of the spectrograph is 100 eV to 2 keV with a spectral resolution of 0.35 nm. The X-ray emission spectrum from femtosecond laser-Cu target interaction has been obtained with the spectrograph on SILEX-Ⅰ. It proves that the spectrograph can meet the design requirements, suitable for researches on soft X-rays produced by laser-plasma interaction.