Abstract: Diagnostics of fusion capsule plasma which usually has a discontinuous radial distribution is a basic problem in laser fusion plasma researches. An Abel inversion method based on basis set expansion was proposed to handle this discontinuous Abel inverse problem. This method expands the radial distribution on a set of basis functions, and then the measurement data can be approximated by a linear combination of Abel transforms of the basis functions. The weighted coefficients of the basis functions were obtained by projected Landweber iteration method. Numerical simulations demonstrate that the proposed method is sufficiently accurate to reconstruct discontinuous radial distribution, and variance of reconstructed result can reach 10-4 for ideal signal. Although some noise were added in measurement data, the inversion result can still reflect discontinuous property of radial distribution accurately.