We report a theoretical calculation of band structure and the superconducting transition temperature of Nb-Zr and Ti-V under pressure. The self-consistent tight binding linear Muffin-Tin orbital method have been used to obtain the band structure. Either Allen-Dynes's formula or McMillan's formula was used to calculate the transition temperature. A simple but a straight forward method was employed to calculate the effect of pressure on Debye temperature or the phonon frequency. From the present study it is found that the value of Tc increases continuously with pressure for both the compounds. The increase in Tc is attributed to the continuous s → d electron transfer under pressure. © 2001 Elsevier Science B.V. All rights reserved.