Dipole and quadrupole strength distribution of ²⁰⁴Pb was investigated via a nuclear resonance fluorescence experiment using bremsstrahlung produced using an electron beam at a kinetic energy of 10.5 MeV at the linear accelerator ELBE. We identified 136 states resonantly excited at energies from 3.6 to 8.4 MeV. Spins of the excited states were deduced by angular distribution ratios of γ rays observed at scattering angles of 90∘ and 127∘ with respect to the incident γ beam. The analysis of the measured γ-ray spectra includes the quasicontinuum of levels at high energy. Monte Carlo simulation of γ-ray cascades were performed to obtain the intensities of inelastic transitions and branching ratios of the ground-state transitions. The present experimental results were used to investigate the electric dipole (E1) strengths by comparison with predictions from the quasiparticle-phonon model with the self-consistent energy density functional.