Instead of the usual zero-width approximation, the finite-width approximation for the resonance, the ρ-ω mesons, is used to investigate the light-cone local QCD sum rules for the form factors of the transitions, ργ*→π0and γγ*→π0. To be more certain, a product of two weight functions is chosen in the method of the analytic continuation by duality to annihilate the uncertainty in the continuum region and the integrand in the integration range not covered by vector-meson dominance and where the theoretical expression may least be trusted. The resultant form factors in the cases for the zero- and finite-widths are almost the same, both agree well with the experimental measurements, and comparison with the results from the Laplacian transformed light-cone sum rules and etc. is discussed.

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