The utility model provides a connection structure of three adjacent blocks for staggered-joint building and a reinforced brickwork of the blocks. The connection structure comprises three hollow blocks and a connecting piece, wherein the three hollow blocks are arranged into upper and lower two layers in such a manner that joints are staggered; the second connecting notch of the middle separator of one hollow block at the upper layer corresponds to the first connecting notches of two end plates, contact with each other, of the two hollow blocks at the lower layer in position and are combined into a combined notch having the shape matched with the shape of the connecting piece; the connecting piece is embedded in the combined notch so that the three hollow blocks are integrally connected together; the brickwork comprises a plurality of layers of hollow blocks built in such a manner that joints are staggered, and a plurality of connecting pieces, without adhesive mortar; the cavities in the hollow blocks are overlaid to form a vertical columnar space; a vertical reinforcement is arranged in the vertical columnar space and concrete is further poured in the columnar space. The connection structure and the reinforced brickwork have the advantages that the fixed connection between the adjacent blocks can be realized by use of the connecting pieces, no adhesive mortar is applied between the adjacent blocks, and the pouring of a core column can be poured immediately after reinforcing while building.