Abstract: Based on type II censored data, generalized lower confidence limit is constructed by two different procedures for the reliability life of a left truncated two-parameter exponential distribution, using the concept of generalized pivotal quantity and generalized confidence interval due to Weerahandi. One procedure is to define the restricted generalized lower confidence limit for the reliability life of a left truncated two-parameter exponential distribution using the generalized lower confidence limit constructed in the case that the location parameter is not restricted. The other is to find the conditional generalized lower confidence limit for the reliability life based on the conditional distribution of generalized pivotal quantity. We investigate the properties of the two lower confidence limits respectively and present simple numerical calculation procedures. Simulation study showns that restricted generalized lower confidence limit gives good coverage probability, coverage probability of conditional generalized lower confidence limit is related to the values of the parameters, but it's mean is bigger and it's variance is smaller in some cases compared with the restricted generalized lower confidence limit.