In this paper, we obtain new explicit expressions for the single and product moments of order statistics from the standard two-sided power (STSP) distribution. These expressions can be used to compute the means, variances and the covariances of order statistics from the STSP distribution. We also have a glance at the application of the results to the lifetimes of the coherent systems. Two real data examples are given to illustrate the flexibility of the STSP distribution.