Chiral switching of the self-assembled domains of CuPc molecules on the Cd(0001) surface has been investigated by means of a low temperature scanning tunneling microscopy (STM). With the coverage increasing, the CuPc molecules show the structural evolutions from an initial gas-like state to a network phase, a square phase, and finally to a compact phase at full monolayer. In the network and square phases, the achiral CuPc molecules reveal both the point chirality and chiral domains. In particular, the chirality of network domain can be switched from one enantiomer to another driven by the electric filed from a STM tip, which can also lead to the lattice rotation of network phase. These results demonstrate that (i) there is strong interaction between the CuPc molecules and STM tip; (ii) the adsorbed CuPc molecules carry considerable net charge or polarizability due to the charge transfer; (iii) the network phase has a low barrier for the interconversion between right- and left-handed domains. Our findings are significant for the understanding and control of the domain's chirality in the self-assembled structures.