  Weyl semimetal defines a material with three dimensional Dirac cones which
appear in pair due to the breaking of spatial inversion or time reversal
symmetry. Superconductivity is the state of quantum condensation of paired
electrons. Turning a Weyl semimetal into superconducting state is very
important in having some unprecedented discoveries. In this work, by doing
resistive measurements on a recently recognized Weyl semimetal TaP under
pressure up to about 100 GPa, we observe superconductivity at about 70 GPa. The
superconductivity retains when the pressure is released. The systematic
evolutions of resistivity and magnetoresistance with pressure are well
interpreted by the relative shift between the chemical potential and paired
Weyl points. Calculations based on the density functional theory also
illustrate the structure transition at about 70GPa, the phase at higher
pressure may host superconductivity. Our discovery of superconductivity in TaP
by pressure will stimulate further study on superconductivity in Weyl
semimetals.
