We study the ab-plane and c-axis charge dynamics of La4Ni3O10 using optical spectroscopy. While a pronounced Drude profile, i.e. metallic response, is observed in the ab-plane optical conductivity σ1ab(ω), the c-axis optical spectra σ1c(ω) exhibit semiconducting behavior. The zero-frequency extrapolation of the optical conductivity σ1(ω → 0) ≡ 1/ρdc gives a resistivity anisotropy of ρc/ρab ≃ 366 at 300 K for La4Ni3O10, which is much larger than the values in iron-based superconductors but comparable to those in high-Tc cuprates. The interband response is also highly anisotropic, showing salient orbital selectivity for light polarized in the ab plane and along the c axis. The interband-transition peaks in both σ1ab(ω) and σ1c(ω) are located at lower energies compared to density-functional-theory predictions, signifying considerable electronic correlations. By investigating the spectral weight transfer, we find that in the pristine state, Coulomb correlations have a marked impact on the charge dynamics of La4Ni3O10, whereas in the density-wave state, a gap opens with the Ni-dz2 orbital being involved.