We have used density functional theory (DFT) and time dependent (TD)-DFT to systematically investigate the dependency of the geometric and vibro-electronic properties of zigzag and armchair-type double-walled boron nitride nanotubes ((0, m)@(0, n) and (m, m)@(n, n)-DWBNNTs) on the interwall distance (Delta R) and the number of unit cells. The results of the calculations showed that their structural stability strongly depends on the interwall distance, but not on the number of unit cells, and the (0, m) @(0, m+9/10) and (m, m) @(n, n) with n= m+5/6 are the most energetically stable structures. The predicted electronic structures for DWBNNTs with cell lengths of one unit exhibit a strong red-shift for the Delta R below similar to 0.4 nm and remain almost constant for the Delta R > 0.45 nm. The calculated nonresonance Raman spectra of (0,6) @(0, n)-DWBNNTs (with cell lengths of one unit and n= 12-18) indicated that the radial breathing modes (RBMs) of inner (0,6) and outer (0, n) tubes are not only diameter dependent, but also exhibit a strong blue-shift for the Delta R below similar to 0.35 nm and rapidly approach zero with increasing Delta R reference to the position of the RBM in the spectrum of the corresponding single wall boron nitride nanotubes, (0, n)-SWBNNTs. The calculated IR spectra of the (0,6) @(0, n)-DWBNNTs did not indicate any significant dependence on the Delta R for n > 13.