Investigated in this paper is an extended (3+1)-dimensional Kadomtsev-Petviashvili equation. We determine the N -soliton solutions of that equation via an existing bilinear form, and then construct the M th-order breather and H th-order lump solutions from the N -soliton solutions using the complex conjugated transformations and long-wave limit method, where N , M , and H are the positive integers. In addition, we develop the hybrid solutions composed of the first-order breather and one soliton, the first-order lump and one soliton, as well as the first-order lump and first-order breather. Through those solutions, we demonstrate the (1) one breather or lump, (2) interaction between the two breathers or lumps, (3) interaction between the one breather and one soliton, (4) interaction between the one lump and one soliton, and (5) interaction between the one lump and one breather. We observe that the amplitude, shape, and velocity of the one breather or lump remain unchanged during the propagation. We also find that the amplitudes, shapes, and velocities of the solitons, breathers, and lumps remain unchanged after the interactions, suggesting that those interactions are elastic.