The detection of the high-frequency peaked BL Lac object (HBL) SHBL J001355.9-185406 (z = 0.095) at high (HE; 100 MeV < E < 300 GeV) and very high-energy (VHE; E > 100 GeV) with the Fermi Large Area Telescope (LAT) and the High Energy Stereoscopic System (H.E.S.S.) is reported. Dedicated observations were performed with the H. E. S. S. telescopes, leading to a detection at the 5.5 sigma significance level. The measured flux above 310 GeV is (8.3 +/- 1.7(stat) +/- 1.7(sys)) x 10(-13) photons cm(-2) s(-1) (about 0.6% of that of the Crab Nebula), and the power-law spectrum has a photon index of Gamma = 3.4 +/- 0.5(stat) +/- 0.2(sys). Using 3.5 years of publicly available Fermi-LAT data, a faint counterpart has been detected in the LAT data at the 5.5 sigma significance level, with an integrated flux above 300 MeV of (9.3 +/- 3.4(stat) +/- 0.8(sys)) x 10(-10) photons cm(-2) s(-1) and a photon index of Gamma = 1.96 +/- 0.20(stat) +/- 0.08(sys). X-ray observations with Swift-XRT allow the synchrotron peak energy in vF(v) representation to be located at similar to 1.0 keV. The broadband spectral energy distribution is modelled with a one-zone synchrotron self-Compton (SSC) model and the optical data by a black-body emission describing the thermal emission of the host galaxy. The derived parameters are typical of HBLs detected at VHE, with a particle-dominated jet.