The ability of the zero-truncated Poisson-Lindley (ZTPL) distribution to analyze zero-truncated count data, including over-dispersion that is common in such data, to provide more accurate modeling and inference is what motivates its use. However, the confidence interval of its parameter has not yet been examined. In this paper, confidence interval estimation based on percentile bootstrap, simple bootstrap, bias-corrected and accelerated bootstrap methods, as well as the bootstrap-t confidence interval, was examined in terms of empirical coverage probability and average length via Monte Carlo simulation. The results indicate that attaining the nominal confidence level using the bootstrap methods was not possible for small and moderate sample sizes regardless of the other settings. Moreover, when the sample sizes were large, the performances of the methods were not substantially different. Overall, it is observed that all bootstrap methods perform well for large sample sizes. Lastly, the bootstrap methods were used to calculate the confidence interval for the zero-truncated Poisson-Lindley parameter via two numerical examples, the results of which match those from the simulation study.