In situ high-pressure x-ray absorption fine structure (EXAFS) measurements on the Zn K-edge in zincblende ZnS are performed up to 31.7 GPa at room temperature using a synchrotron radiation x-ray re-focused by a polycapillary half-lens in the classic energy-scanning transmission mode. The present XAFS data illustrate that ZnS undergoes a phase transition from zincblende F43m to rocksalt Fm3m at 16.9 GPa, accompanied by the increase of the first shell coordination number of the absorption zinc atoms and the unit-cell volume collapse of similar to 14%. The isothermal equation of state of the F (4) over bar 43m ZnS is well presented by the third-order Birch-Murnaghan equation of state with V-0 = 158.6 +/- 0.8 angstrom(3), B-0 = 87 +/- 5GPa and B-0' = 4 (fixed). The high-pressure behavior of ZnS from the XAFS spectra is consistent with the previous high-pressure XRD results. In addition, the present experimental method demonstrates that the large divergent x-ray micro-beam induced by a polycapillary half-lens can suppress effectively the glitches from single crystal diamond anvil and improve significantly the quality of the XAFS data, which will shed light on the high-pressure XAFS applications.