We observed the first unidentified TeV \gamma -ray source TeV J2032 + 4130 with Suzaku . Owing to Suzaku ’ s high sensitivity for detection of diffuse X-ray emission , we found two small structures in the TeV emitting region . One of them is coincident with a \gamma -ray pulsar PSR J2032 + 4127 , which was discovered by the Fermi Gamma-ray Space Telescope . By subtracting contribution of point sources estimated by Chandra data , we obtained diffuse X-ray spectrum . The X-ray spectrum can be reproduced by a power-law model with a photon index of \sim 2 , and an X-ray flux of 2 \times 10 ^ { -13 } erg s ^ { -1 } cm ^ { -2 } . The ratio of the \gamma -ray flux to the X-ray flux is about 10 . If the origin of the TeV \gamma -ray is inverse Compton scattering of microwave background by high energy electrons , the ratio corresponds to the magnetic field strength of \sim 1 \mu G. However , the smaller size of the X-ray emission than that of the TeV emission suggests that energy loss of the electrons can explain the large ratio of the \gamma -ray flux with a reasonable magnetic field strength of a few \mu G .