The sensitivity design of the spaceborne hyperspectral imager is crucial for obtaining high-quality image data. To reduce the costs of size, weight, cost, and development cycle caused by excessive increase in aperture, it is necessary to accurately estimate the system sensitivity during overall design. We use semi physical simulation method, establish a SNR (Signal Noise Rate) model of a hyperspectral imager under the typical condition. We apply the model to calculate sensitivity, the result shows that the system requires a minimum SNR of 170 with a minimum aperture of 450mm under design requirements of 10m spatial resolution, sun-synchronous orbit etc. We analyze and provide the overall system configuration with fully reflective optical system and convex glitter grating and also give sensitivity related system parameter boundary conditions. The results of ground testing and preliminary imaging testing in orbit after system integration show that the hyperspectral sensitivity model is accurate and the system sensitivity meets the requirements of the indicators. Models and design ideas can help promote rapid system customization design of commercial aerospace hyperspectral payloads to improve developing efficiency and reduce costs.