Pb is widely used as grid material for lead-acid batteries, an electrowinning electrode and a nuclear radiation shield. To improve the performance of these materials, alloying elements such as Ag, Sb, and Ca are commonly added. Pb's conductivity and strength can be improved using Al as an alloying element. However, the phase diagram of the Pb-Al alloy is characterized by the large liquid-liquid and liquid-solid miscibility gaps. When a homogeneous single-phase Pb-Al liquid is cooled into the miscibility gaps, Al-rich droplets/particles precipitate first from the melt, causing the Pb-Al alloy to form a microstructure with coarse Al-rich particles or serious phase segregation. Understanding the evolution of microstructure in the liquid-solid phase separation has remained a scientific challenge thus far. The solidification of the Pb-Al alloy is investigated using directional solidification experiments in this work. A numerical model is developed to describe the microstructure formation in a directionally solidified liquid-solid phase separation alloy using the population dynamics method. The evolution of the microstructure is simulated. The simulation results agree well with the experimental results. They show that a supercooling zone appears in front of the solidification interface, where the liquid-solid phase separation of the Pb-Al alloy occurs. In this zone, Al-rich particles (dispersed phase) form and grow by solute diffusing as they move toward the solidification interface. The nucleation rate and the number density of Al-rich particles increase as the solidification rate increases, whereas the average radius of the particles decreases. The Al-rich particles' Stokes movement velocity has the same direction as the melt's solidification velocity, resulting in an enrichment of Al-rich particles in front of the solidification interface. Because of the convective flow of the melt in front of the solidification interface, the cooling rate of the melt is unevenly distributed along the radial direction, resulting in an uneven distribution of nucleation rate, number density, and average radius of Al-rich particles. The formation of a solidification microstructure with the dispersive distribution of Al-rich particles is dependent on the solidification rate being fast enough to ensure that all size particles in the liquid-solid phase separation region move toward the solidification interface under the effect of the Stokes movement of Al-rich particles and the convective flow of melt.