Abstract: The motion parameters of the arc reignition have a significant impact on the HVDC relay's performance. The primary method of quenching arcs in high-voltage DC relays is magnetic blowing by a permanent magnet. This paper establishes a magnetohydrodynamic arc model of high-voltage DC relays based on the theory of magnetohydrodynamics and simulates and analyzes the dynamic process of arc reignition under specific electric field strengths in order to investigate the impact of permanent magnet magnetic field distribution on arc motion characteristics. The evolution of plasma during arc initiation to arc extinction is obtained. Further,the variation of characteristic parameters such as airflow field, arc potential and air pressure field during arc motion is systematically studied. The results show that the magnetic induction intensity in the contact area presents a non-uniform distribution of large in the middle and small on both sides under a strong magnetic field environment. The arc form changes substantially, the arc blowing effect is much enhanced, and the arc burning time is greatly reduced as the magnetic field intensity increases. Arc extinguishing is made easier by increasing the Lorentz force, speeding up the arc motion, shortening the time it takes for the arc center to leave the contact gap, weakening the arc ablation ability, and increasing the potential. This provides a theoretical basis for the structural design of the new high-voltage DC relay arc extinguishing system.