Synthesis of calcium-substituted sodium borophosphate glasses with compositions $x{\rm CaO} − (30 − x){\rm Na}_2{\rm O} −35{\rm B}_2{\rm O}_3−35{\rm P}_2{\rm O}_5$ ($x = 0$, 2, 5, 7 and 10 mol%, abbreviated as CNV$x$) containing additional 1.0 mol% of V$_2$O$_5$ following a melt-quench method has been carried out. Different analytical techniques viz. wide angle X-ray diffraction (to confirm noncrystallinenature), ultraviolet–visible spectroscopy (for optical band gap analysis), infrared absorption spectroscopy (for structural analysis) and differential thermal analysis (to evaluate characteristic temperatures) were employed to characterizethe synthesized compositions. The optical band gap is calculated for both indirect allowed and indirect forbidden transitions. The values of the band gap decrease with increasing concentration of CaO (from 5 to 10 mol%) at the cost of Na$_2$O. The cut-off wavelength and Urbach’s energy are determined from the optical absorption spectra and were related to the structural changes occurring in these glasses with an increase in CaO content. The results obtained from Fourier-transform infrared studies confirm that V$_2$O$_5$ and CaO play the role of network modifier oxides. Also, the significant shifting in IR bands with an increase in CaO content in the glass matrix suggests the formation of a new boron–oxygen ring. From differential scanning calorimetry measurements it is observed that substitution leads to the increase in natural bond orbitals,high degree cross-linking and thus strengthens the glass network. Glass transition temperature ($T_{\rm g}$) is found to increase from 483 to 522$^{\circ}$C. Electrical and dielectric properties are analysed using dc conductivity and impedance spectroscopy. Using impedance spectroscopy, different dielectric parameters i.e. dielectric loss ($\epsilon^{\prime}$), electrical modulus ($M^∗$) and ac conductivity ($\sigma_{\rm ac}$) etc. are evaluated as a function of frequency, temperature and composition. The frequency dependence of impedance exhibits the non-Debye relaxation behaviour and the total conductivity obeys Jonscher’s power law.