The imagery vendors of the most advanced remote sensing satellites usually only provide the coefficients of rational function model (RFM) to replace the sensor model and the precise imaging parameters (orbit parameter, attitude parameter, and so on). So, the rigorous imaging model was limited to use in the geometric correction of remote sensing image. The RFM method could obtain a better correction performance in most cases. However, when the image contains few numbers or uneven distribution of ground control points (GCPs), such as infrared image, the RFM method could not obtain the expected performance. Therefore, a geometric correction method for linear pushbroom infrared imagery using compressive sampling (CS) is proposed. The core idea of the proposed method is to use the equivalent bias angles to approximate the influence of the errors (thermal distortion, optical distortion, assembly error, satellite orbit errors, attitude errors, and so on) in the imaging process and adopt the CS method to recover the equivalent bias angle signals. Most of the data are processed scene by scene with enough GCPs for each scene in conventional methods. This restriction is broken by using the sparsity of equivalent bias angle signals in the proposed method. The infrared images from the Hyperion of EO-1 are used as experiment data, and the results of experiments demonstrate the feasibility and superior performance of proposed method.