This paper considers the trimmed least squares estimator of the autoregression parameter in the unstable AR(1) model: Xulcorner=ØXulcorner+$varepsilon$ulcorner, where $varepsilon$ulcorner are iid random variables with mean 0 and variance $sigma$$^2$> 0, and Ø is the real number with │Ø│=1. The trimmed least squares estimator for Ø is defined in analogy of that of Welsh(1987). The limiting distribution of the trimmed least squares estimator is derived under certain regularity conditions.