We report the discovery of an active intermediate-mass black hole (IMBH) candidate in the center of nearby barred bulgeless galaxy NGC 3319. The point X-ray source revealed by archival Chandra and XMM-Newton observations is spatially coincident with the optical and UV galactic nuclei from Hubble Space Telescope observations. The spectral energy distribution derived from the unresolved X-ray and UV-optical flux is comparable with active galactic nuclei rather than ultraluminous X-ray sources, although its bolometric luminosity is only 3.6 x 10(40) erg s (1). Assuming an Eddington ratio range between 0.001 and 1, the black hole mass (M-BH) will be in the range 3 x 10(2) -3 x 10(5) M-circle dot, placing it in the so-called IMBH regime and making it possibly one of the lowest reported so far. Estimates from other approaches (e.g., fundamental plane, X-ray variability) also suggest M-BH less than or similar to 10(5) M-circle dot. Similar to other BHs in bulgeless galaxies, the discovered IMBH resides in a nuclear star cluster with mass of similar to 6 x 10(6) M-circle dot. The detection of such a low-mass BH offers us an ideal chance to study the formation and early growth of SMBH seeds, which may result from the bar-driven inflow in late-type galaxies with a prominent bar such as NGC. 3319.