A design for strap lap bond joints of wood powder/polyethylene composites (WP/PE) was proposed. The effects of combined treatment on surface properties of WP/PE and failure modes of WP/PE bonded by epoxy and acrylic ester were investigated. A finite element model of strap lap bond joints of WP/PE was established based on the elastoplasticity finite element method, and the effects of lap length and adhesive (epoxy and acrylic ester) on stress distributions and comprehensive displacements of strap lap bond joints of WP/PE were investigated. The results demonstrated that the bonding interface roughness of WP/PE was enhanced by the combined surface treatment. Active oxygen-containing functional groups were introduced to the sample surface. The finite element simulation results revealed that the Mises equivalent stress peaks and comprehensive displacements of strap lap bond joints were concentrated in lap zone ends and board connections, the stress distribution was independent of the lap length, and the Mises equivalent stress peaks and comprehensive displacements were independent of the adhesive.