By using some distributional properties, we obtain some results on recurrence relations for single and product moments of order statistics from doubly truncated Burr XII distribution. These results complement earlier results of Begum and Parvin [2002], as well as, generalize results obtained by Balakrishnan and Gupta [1998], Balakrishnan et al. [1994], and Saran and Pushkarna [1999]. Simulation results are consistent with those obtained by Begum and Parvin [2002] and are given for single and product moments in Tables 1 and 2. Applications to least squares estimation of the Best Linear Unbiased Estimates of location-scale parameters involving singly and doubly censored life-testing data are considered. The estimation results compare favorably with those by Balakrishnan and Gupta [1998] in estimating the scale parameter of the censored data using the exponential distribution.