Abstract: The statistical moments of response are one of the main ways to describe the response of a random structural system. Compared with the probability density function (PDF) of the response, the statistical moments of the structural response can be easily obtained, and therefore it is quite concerned by researchers. Among them, the efficient calculation method for statistical moments of structural response has always been a hot research topic. The conjugate unscented transformation method (CUT), which keeps the tradeoff of accuracy and efficiency, is used as the basis in this paper. By introducing the normal-nonnormal transformation (NNT), the first type of extended conjugate unscented transformation method (ECUTI) is proposed, which is appropriate for the statistical moment estimation of random systems involving arbitrary random variables. Secondly, based on the high dimensional reduction model (HDRM) and the ECUTI, the second type of extended conjugate unscented transform method (ECUTⅡ) which is suitable for the statistical moment estimation of random system of arbitrary dimensions is proposed. The proposed methods are verified through three numerical examples. The results of examples show that: The two types of proposed methods can satisfy the accuracy and efficiency on the basis of expanding the scope of application of the CUT; The ECUTI and the ECUTⅡ are recommended for statistical moment estimation of the response for low-dimensional and high-dimensional problems, respectively.