In this work, we study the flavor-changing neutral-current process Bc→Ds*(→Dsπ)ℓ+ℓ− (ℓ=e, μ, τ). The relevant weak transition form factors are obtained by using the covariant light-front quark model, in which the main inputs, i.e., the meson wave functions of Bc and Ds*, are adopted as the numerical wave functions from the solution of the Schrödinger equation with the modified Godfrey-Isgur model. With the obtained form factors, we further investigate the relevant branching fractions and their ratios, and some angular observables, i.e., the forward-backward asymmetry AFB, the polarization fractions FL(T), and the CP-averaged angular coefficients Si and the CP asymmetry coefficients Ai. We also present our results of the clean angular observables P1,2,3 and P4,5,6,8′, which can reduce the uncertainties from the form factors. Our results show that the corresponding branching fractions of the electron or muon channels can reach up to 10−8. With more data being accumulated in the LHCb experiment, our results are helpful for exploring this process, and deepen our understanding of the physics around the b→sℓ+ℓ− process.