We report the giant anisotropic strain response in vibrational modes of ultrathin black phosphorus (BP). A modified bending technique was employed to apply precise uniaxial tensile strain to zigzag or armchair directions of the BP flakes. The Raman shift rates of A¹_g, B_2g and A²_g  modes of BP are significantly distinct for strain applied along zigzag or armchair directions. For the applied strain along zigzag direction, the Raman shift rate and the Grüneisen parameter of the B_2g mode can reach a remarkable value of ~-11 cm^-1/% strain and ~3.7 respectively, which are the largest among all the reported values in two-dimensional materials. The density functional theory calculations were performed to understand the exceptional anisotropic strain response in the vibrational modes of BP. It is found that not only the bond lengths but also the bond angels are changed in BP upon applied strain which lead to giant anisotropic response in mode B_2g . Furthermore, we demonstrate a simple method based entirely on the strained BP and conventional Raman spectroscopy to determine the crystallographic orientations of BP without the aid of polarization Raman spectroscopy. This work may pave a way to study the strain-induced anisotropic electrical conductance and the magnetotransport properties of BP.