In order to elucidate the magnetism and Li diffusion in LiFePO₄, we have measured muon-spin rotation and relaxation (μ⁺SR) spectra for the polycrystalline LiFePO₄ sample in the temperature range between 1.8 and 500 K. Below T_N ∼ 52 K, two oscillatory signals together with one fast relaxation signal were clearly found in the zero-field (ZF) μ⁺SR spectrum. The three signals are reasonably explained using an antiferromagnetic (AF) spin structure proposed by neutron measurements, because electrostatic potential calculations suggests multiple different muon sites in the LiFePO₄ lattice. However, the AF ordered moment estimated from μ⁺SR was about 3/4 of that reported by neutron, probably due to a different time window between the two techniques. In the paramagnetic state, ZF and longitudinal-field (LF) μ⁺SR spectra exhibited a dynamic nuclear field relaxation. From the temperature dependence of the field fluctuation rate, a diffusion coefficient of Li⁺ ions (D_Li) at 300 K was estimated about 3.6×10^-10 cm²/s, assuming that diffusing Li⁺ ions jump between the regular site and interstitial sites.