A compact broadband Compton spectrometer with high spectral resolution has been designed to detect spectra of laser-driven high-flux gamma rays. The primary detection range of the gamma-ray spectrum is 0.5 MeV–13 MeV, although a secondary harder gamma-ray region of 13 MeV–30 MeV can also be covered. The Compton-scattered electrons are spectrally resolved using a curved surface detector and a nonuniform magnetic field produced by a pair of step-like magnets. This design allows a compact structure, a wider bandwidth, especially in the lower-energy region of 0.5 MeV–2 MeV, and optimum spectral resolution. The spectral resolution is 5%–10% in the range 4 MeV–13 MeV and better than 25% in the range 0.5 MeV–4 MeV (with an Al converter of 0.25 mm thickness and a collimator of 1 cm inner diameter). Low-Z plastic materials are used on the inner surface of the spectrometer to suppress noise due to secondary X-ray fluorescence. The spectrometer can be adjusted flexibly via a specially designed mechanical component. An algorithm based on a regularization method has also been developed to reconstruct the gamma-ray spectrum from the scattered electrons.