The optical conductivity $sigma_{1}(omega)$ of Eu$_{1-x}$Ca$_{x}$B$_{6}$ has been obtained from reflectivity and ellipsometry measurements for series of compositions, $0leq xleq 1$. The interband part of $sigma_{1}(omega) $ shifts continuously to higher frequency as Ca-content $x$ increases. Also the intraband spectral weight of $sigma_{1}(omega)$ decreases rapidly and essentially vanishes for $xgeq x_{c}=0.35$. These results show that the valence band and the conduction band of Eu$_{1-x}$Ca$_{x}$B$_{6}$ move away from each other such that their band overlap decreases with increasing Ca-substitution. As a result, the electronic state evolves from the semimetallic structure of EuB$_{6}$ to the insulating CaB$_{6}$ where the two bands are separated to open a finite gap ($simeq 0.25$ eV) at the X-point of the Brillouin zone.
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