An elliptical crystal spectrometer has been developed based on elliptical focusing principle to diagnose spatial spectrum of X-ray of Z-pinch plasma. An elliptically bent Si(111) crystal was employed with 1348 mm focal length, 0.9480 eccentricity, 30°～54° Bragg angel, 54°～103° viewing angle and 0.31～0.51 nm spectral range. A semicircle film carrier with 50 mm radius was designed to receive spectral signals. The influence of elliptical disperson on spectral resolution was analyzed. The first experiment was carried out on the Yang accelerator. The transition spectrum of Ar jet plasma X-ray was recorded. The measured wavelength is accorded with the theoretical value with spectral resolution λ/Δλ of 300～500.