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In order to discuss the load capacity and displacement of masonry constructed with recycled concrete and self-insulation blocks, one type of 10.6 MPa compressive strength block and three kinds of mortar with M15, M10, and M5 compressive strengths are selected. The constitutive model and corresponding parameters selection of different materials in the ABAQUS numerical simulation are analyzed, and the numerical simulation analysis and experimental tests of the load capacity and displacement of masonry constructed with mortars of different strengths are carried out. The results show that masonry compression failure is controlled by the mortar or block that has the lower compressive strength. The displacement of masonry increases with the mortar compressive strength increase, and the higher mortar compressive strength is beneficial for improving the load capacity and displacement of masonry. Reasonable selection of the constitutive model and parameters will help to obtain reasonable results for the ABAQUS numerical simulation. Construction quality and loading method will affect the load capacity and displacement of the masonry. The above conclusion can provide reference for the engineering application of recycled concrete and self-insulation blocks.