The growth and collapse of a bubble near composite boundaries are studied using the boundary element method. The composite boundary in the present report represents a rigid body floating on the free surface. It is shown that when the mass of the floating body is sufficiently heavy, the bubble behavior is similar to that near rigid boundaries: the bubble deforms while moving toward the floating body, and the liquid jet penetrates the bubble surface in the final stage of the collapse. On the other hand, when the mass is moderate, the bubble collapses nearly spherically without translation. The results also show that the high pressure region is produced on the body surface after the penetration of liquid jet.