We report the detection, with the CANGAROO-III imaging atmospheric Cherenkov telescope array, of a very high energy gamma-ray signal from the unidentified gamma-ray source HESS J1614−518, which was discovered in the H.E.S.S. Galactic plane survey. Diffuse gamma-ray emission was detected above 760 GeV at the 8.9σ level during an effective exposure of 54 hr from 2008 May to August. The spectrum can be represented by a power law: (8.2 ± 2.2 stat ± 2.5 sys ) × 10 −12 × (E/1 TeV) −γ cm −2 s −1 TeV −1 with a photon index γ of 2.4 ± 0.3 stat ± 0.2 sys , which is compatible with that of the H.E.S.S. observations. By combining our result with multiwavelength data, we discuss the possible counterparts for HESS J1614−518 and consider radiation mechanisms based on hadronic and leptonic processes for a supernova remnant (SNR), stellar winds from massive stars, and a pulsar wind nebula (PWN). Although a leptonic origin from a PWN driven by an unknown pulsar remains possible, hadronic-origin emission from an unknown SNR is preferred.