Different from the existing mathematical models for switched systems, where the switching from one subsystem to another subsystem is finished instantly, in this paper it is assumed that the switching is a transfer process. Moreover, there exists a basic transfer subsystem such that in the transfer process, the transfer subsystem is active. Based on the model of switched linear discrete-time systems under constrained switching, this paper studies the reachability of such systems. A necessary and sufficient geometric criterion for reachability of such systems is established. Finally, an example is given to illustrate the results.