Diagnosability of a multiprocessor system is one important study topic. In 2012, Peng et al. proposed the g-good-neighbor diagnosability that restrains every fault-free node to contain at least g fault-free neighbors. The locally twisted cube LTQ_n has many good properties. In this paper, we show that the 1-good-neighbor connectivity κ~1(LTQ_n) = 2n-2 and the 1-good-neighbor diagnosability of LTQ_n is 2n-1 under the PMC model for n ≥ 4 and the MM~*model for n ≥ 5.