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The development of large-format detector arrays with background-limited performance is of particular interest at the terahertz（THz） band, which is a unique band in search of our cosmic origins. With high sensitivity and being more promising in the pixel number and multiplexing technology, superconducting kinetic inductance detectors（KID） are emerging as a major choice of detectors of this type. Here we fabricate three-THz-band（0.35/0.85/1.4 THz） KIDs on a single chip from a 120-nm-thick aluminum（Al） superconducting film and measure photon-noise-limited performance and intrinsic generation-recombination noise at high（>1 p W） and low（<1 f W） optical radiation power, respectively. Their responses to blackbody（optical） radiation are proven to be purely from photons compared with the responses of two dark KIDs intentionally arranged on the same detector chip. The lowest optical noise equivalent power（NEP） reaches 6×10-18 W/Hz0.5 and the optical coupling efficiency is in the range of 49%-56% for the three KIDs, which are in good agreement with the simulation results.