Master-slave control is one of the key methods for realizing the control of robot-assisted puncture operations. However, due to the complexity and diversity of puncture-assisted robots as well as their sensing and feedback methods, there exist significant challenges in the rapid construction of master-slave control for surgical robot systems. This paper proposes a rapid construction method for master-slave control of puncture surgical robots, which enables a rapid construction of the master-slave motion mapping and a rapid implementation of the master-slave control. Firstly, a coordinate system for the object motion is established, and the relative position transformation chain for the coordinate transformations of object motion mapping is further defined and constructed to realize explicit expression of the coordinate transformations of the object motions, and thus achieving the rapid construction of the motion mapping. Secondly, a rapid construction strategy for the master-slave motion mapping based on an intuitive mapping model is proposed. For the slave objects with various sensing and feedback modes, the relative position transformation chain for the master-slave motion mapping is quickly constructed to enable the calculation of the multiple coordinate transformations for the master-slave control and to further realize the rapid realization of the customized and diversified master-slave control. Experimental studies are then conducted using the proposed method, and the rapid constructions and implementations of 4 types of the master-slave control for two master objects and two slave objects are implemented, respectively. The experimental results show that: The proposed rapid construction strategy for the master-slave control mapping can realize a rapid construction of the master-slave motion mapping with various sensing feedbacks, and 4 relative position transformation chains for the master-slave motion mapping are obtained, where each transformation chain represents an independent type of the master-slave control to accommodate the requirements of different application scenarios; through the control calculation of the multiple coordinate transformations based on the relative position transformation chains, the rapid implementation of the master-slave control is achieved, which verifies the feasibility and practicality of the proposed rapid construction method for the master-slave control.