The design and measurement of a concave grating spectrometer chip have been studied in this thesis. By using the theory of diffraction grating, we designed the concave grating which has been fabricated on a silicon wafer by x-ray lithography technique. Firstly, a design principle and rule based on the theory of diffraction grating were stated, and we took Rowland circle into our basic design concept, then analyzed the optical performance of concave grating by series expansion. We also brought out the idea of fabricating the concave grating by x-ray lithography technique, and the concave grating has been presented in this thesis. Finally, we measured the optical property of the concave grating spectrometer chip. Its results: resolution of 0.6nm and channel spacing of 0.4nm match our design.