We report high-pressure Raman, synchrotron x-ray diffraction, and electrical transport studies on Weyl semimetals NbP and TaP along with first-principles density functional theoretical (DFT) analysis. The frequencies of first-order Raman modes of NbP harden with increasing pressure and exhibit a slope change at P c ∼ 9 GPa. The pressure-dependent resistivity exhibits a minimum at P c. The temperature coefficient of resistivity below P c is positive as expected for semimetals but changes significantly in the high-pressure phase. Using DFT calculations, we show that these anomalies are associated with a pressure-induced Lifshitz transition, which involves the appearance of electron and hole pockets in its electronic structure. In contrast, the results of Raman and synchrotron x-ray diffraction experiments on TaP and DFT calculations show that TaP is quite robust under pressure and does not undergo any phase transition.