We consider the problem of estimating the density D of a population of objects or animals with ungrouped data from line transect sampling. We present a method of deriving an approximate confidence interval for D. This confidence interval requires the estimation of a certain standard deviation by the bootstrap method. It also requires the estimation with negligible bias of the value f(O) of a density functions. We present a method of bias reduction in the case wheref(O) is estimated by the Fourier series method. Monte Carlo simulations indicate that the coverage rates are smaller than their nominal values, but the bias reduction offers an improvement, especially when f is peaked at 0, or when it is long-tailed.