After successfully growing single-crystal TaP, we measured its longitudinal resistivity （Pxx） and Hall resistivity （Pyx） at magnetic fields up to 9 T in the temperature range of 2-300 K. At 8 T, the magnetoresistance （MR） reached 3.28 ×10^5% at 2 K, 176% at 300 K. Neither value appeared saturated. We confirmed that TaP is a hole-electron compensated semimetal with a low carrier concentration and high hole mobility ofμh=3.71 × 105 cm2/V s, and found that a magnetic-field-induced metal-insulator transition occurs at room temperature. Remarkably, because a magnetic field （H） was applied in parallel to the electric field （E）, a negative MR due to a chiral anomaly was observed and reached -3000% at 9 T without any sign of saturation, either, which is in contrast to other Weyl semimetals （WSMs）. The analysis of the Shubnikov-de Haas （SdH） oscillations superimposed on the MR revealed that a nontrivial Berry＇s phase with a strong offset of 0.3958, which is the characteristic feature of charge carriers enclosing a Weyl node. These results indicate that TaP is a promising candidate not only for revealing fundamental physics of the WSM state but also for some novel applications.