  We investigate the finite groups $G$ for which $\chi(1)^{2}=|G:Z(\chi)|$ for
all characters $\chi \in Irr(G)$ and $|cd(G)|=2$, where $cd(G)=\{\chi(1)| \chi
\in Irr(G)\}$. We call such a group a GVZ-group with two character degrees. We
establish bijections between the sets of characters of some groups obtained
from a GVZ-group with two character degrees. Additionally we obtain some
alternate characterizations of a GVZ-group with two character degrees and we
construct a GVZ-group having the character degree set $\{1,p\}$.
