Abstract: To accurately estimate the propagating features of the Lamb waves in composite honeycomb structures, a sparse representation and reconstruction method is proposed for the frequency-wavenumber calculation. Firstly, according to the theoretical scattering model of the Lamb waves, the sparse formulation is established regarding the Lamb wave representation in the frequency-wavenumber domain. Secondly, taking the sparse distribution as a constraint, the sparse function can be solved by the basis pursuit denoising method, with the use of the l₁ norm optimization. Finally, the dispersion relation can be extracted via tracing the ridge in the reconstructed wave frequency-wavenumber domain. An experiment is carried out on an aircraft wing made of composite honeycomb. It is shown that the proposed method is reliable to guarantee the estimation accuracy of the propagation characteristic curve under finite numbers of testing, thus can be used in engineering applications.