Shallow water waves are studied for the applications in hydraulic engineering and environmental engineering. In this paper, a (2+1)-dimensional extended shallow water wave equation is investigated. Hybrid solutions consisting of H -soliton, M -breather and J -lump solutions have been constructed via the modified Pfaffian technique, where H , M and J are the positive integers. One-breather solutions with a real function ϕ ( y ) are derived, where y is the scaled space variable, we notice that ϕ ( y ) influences the shapes of the background planes. Discussions on the hybrid waves consisting of one breather and one soliton indicate that the one breather is not affected by one soliton after interaction. One-lump solutions with ϕ ( y ) are obtained with the condition, where k 1 R and k 1 I are the real constants, we notice that the one lump consists of two low valleys and one high peak, as well as the amplitude and velocity keep invariant during its propagation. Hybrid waves consisting of the one lump and one soliton imply that the shape of the one soliton becomes periodic when ϕ ( y ) is changed from a linear function to a periodic function.