Geomagnetic navigation has received widespread attention in recent years due to its advantages of high autonomy, good concealment, no accumulated error, and all-weather availability. Traditional geomagnetic matching navigation methods, such as Magnetic Contour Matching (MAGCOM) and Iterative Closest Contour Point (ICCP), are primarily designed for navigation within a single altitude. However, in practical environment, platforms like aircraft and submarines may need to traverse multiple altitudes, leading to the failure of traditional algorithms. To address this issue, this paper proposes a three-dimensional geomagnetic matching navigation algorithm using Particle Swarm Optimization (PSO), which can achieve trajectory matching in three-dimensional space under low noise conditions. Simulation experiments have demonstrated that, regardless of whether the carrier is moving horizontally or across altitude layers, the matching error under noise conditions of 20 nT and below is lower than the Inertial Navigation System (INS) error set in the experiment, achieving ideal results.