Context : The detection of gamma-rays in the very-high-energy ( VHE ) range ( 100 GeV-100 TeV ) offers the possibility of studying the parent population of ultrarelativistic particles found in astrophysical sources , so it is useful for understanding the underlying astrophysical processes in nonthermal sources . Aims : The discovery of the VHE gamma-ray source HESS J1507-622 is reported and possibilities regarding its nature are investigated . Methods : The H.E.S.S . array of imaging atmospheric Cherenkov telescopes ( IACTs ) has a high sensitivity compared with previous instruments ( \sim 1 % of the Crab flux in 25 hours observation time for a 5 \sigma point-source detection ) and has a large field of view ( { \sim } 5 ^ { \circ } in diameter ) . HESS J1507-622 was discovered within the ongoing H.E.S.S . survey of the inner Galaxy , and the source was also studied by means of dedicated multiwavelength observations . Results : A Galactic gamma-ray source , HESS J1507-622 , located { \sim } 3.5 ^ { \circ } from the Galactic plane was detected with a statistical significance > 9 \sigma . Its energy spectrum is well fitted by a power law with spectral index \Gamma = 2.24 \pm 0.16 _ { stat } \pm 0.20 _ { sys } and a flux above 1 TeV of ( 1.5 \pm 0.4 _ { stat } \pm 0.3 _ { sys } ) \times 10 ^ { -12 } cm ^ { -2 } s ^ { -1 } . Possible interpretations ( considering both hadronic and leptonic models ) of the VHE gamma-ray emission are discussed in the absence of an obvious counterpart . Conclusions :