A novel joining technology was applied to join Fiber Reinforced Polymer (FRP) and AZ31B Mg alloy, which combined the laser-arc welding source and riveting joining methods. The design idea of the stepped rivet was proposed. The weld morphology, mechanical properties, microstructures of welds under two different rivet structures were investigated. FRP and AZ31B Mg could be joined successfully by the new hybrid joining method when it used two different structural rivets. The maximum tensile shear load of the joint under stepped rivet of small size was only 800 N, while that of the joint under stepped rivet of the larger size could reach 1419 N, nearly 90% of that of FRP. There was no reaction between the FRP plate and AZ31B rivet. While the magnesium elements and aluminum elements diffused and reacted with other elements in the FRP plate/AZ31B plate interface.