Small-satellite constellations can combine wide-field survey and rapid follow-up, creating a strong demand for lightweight and compact X-ray telescopes. A lightweight and compact Wolter-I X-ray telescope (CXT) is presented for transient-source polarimetric observations in the 1–8 keV band. The design goals include a preliminary mass budget of ∼2 kg, an angular resolution better than 65″, and a focal length of ∼800 mm. The telescope design and its associated lightweighting approach are described. Based on Monte Carlo simulations and ray-tracing methods, this work optimized the key parameters in terms of the relevant performance metrics and determined a 95-shell nested mirror configuration satisfying the design requirements. On this basis, a more detailed and systematic analysis of the performance of the final design was carried out. In addition, simulations using the main parameters of the Einstein Probe Follow-up X-ray Telescope (EP-FXT) were carried out and compared with the experimental results of EP-FXT to validate the reliability of the simulation method. This work also analyzes the impact of the proposed CXT design on the transmission of polarization information, providing a reference for subsequent detector-level polarization reconstruction.