We present numerical simulations of the propagation of ultra-high-energy cosmic rays (UHECRs) above 10¹⁹ eV in a structured extragalactic magnetic field (EGMF) and simulate their arrival distributions at the Earth. We use the IRAS PSCz catalog in order to construct a model of the EGMF and source models of UHECRs, both of which reproduce the local structures observed around the Milky Way. We also consider modifications of UHECR arrival directions by the Galactic magnetic field. We follow an inverse process of their propagation from the Earth and record the trajectories. This enables us to calculate only trajectories of UHECRs arriving at the Earth, which saves CPU time. From these trajectories and our source models, we construct arrival distributions of UHECRs and calculate their harmonic amplitudes and two-point correlation functions. We estimate the number density of sources that best reproduces the Akeno Ground Air Shower Array (AGASA) observation. As a result, we find that the most appropriate number density of the sources is ~5 × 10^-6 Mpc^-3. This constrains the source candidates of UHECRs. We also demonstrate sky maps of their arrival distribution with the event number expected by future experiments and examine how the EGMF affects their arrival distribution. A main result is the diffusion of clustering events, which are obtained from calculations in the absence of the EGMF. This tendency allows us to reproduce the observed two-point correlation function better.