The invention discloses a floating-type device for the rock embedment mounting of a steel pipe pile in water. The floating-type device for the rock embedment mounting of the steel pipe pile in the water comprises a platform, and also comprises floating boxes, multiple groups of trusses, four hydraulic supporting columns, two tracks, a portal frame, a lifting mechanism and a drilling mechanism, wherein the floating boxes are longitudinally arranged fixedly on the two sides of the lower surface of the platform at an interval; the multiple groups of trusses are fixedly connected with the floating boxes on the two sides and are transversely arranged at an interval; the four hydraulic supporting columns are arranged at the four corners of a panel of the platform, and further, the upper ends of the four hydraulic supporting columns penetrate through the platform and the lower ends of the four hydraulic supporting columns are inserted into the water to a surficial rock; the two tracks are arranged on the platform, are parallel to each other and longitudinal and are further perpendicular to the two ends of the platform; the portal frame is arranged on the two tracks and can be moved along the tracks; the lifting mechanism is arranged on a transverse beam of the portal frame and is used for lifting to convey a steel pipe for position alignment; the drilling mechanism is fixedly arranged on a central beam of the portal frame. A construction method of the floating-type device for the rock embedment mounting of the steel pipe pile in the water comprises the following steps of performing position alignment; lifting a steel-pipe-pile pile casing, and enabling a drill rod to penetrate into the steel-pipe-pile pile casing; punching. The floating-type device which is provided by the invention is high in bearing capacity, is convenient to move, can be used for preventing the platform from being influenced by wave impact and a drilling dynamic load to generate shake, further, is simple in structure, easy and feasible to operate, and is applicable to various waterborne operations.