A non-regular tree T with a prescribed branching sequence (s₁,s₂,...,s_n) is a rooted and ordered tree such that its internal nodes are numbered from 1 to n in preorder and every internal node i in T has s_i children. Recently, Wu et al. (2010) introduced a concise representation called RD-sequences to represent all non-regular trees and proposed a loopless algorithm for generating all non-regular trees in a Gray-code order. In this paper, based on such a Gray-code order, we present efficient ranking and unranking algorithms of non-regular trees with n internal nodes. Moreover, we show that the ranking algorithm and the unranking algorithm can be run in O(n²) time and O(n²+nS_n-1) time, respectively, provided a preprocessing takes O(n²S_n-1) time and space in advance, where $S_{n-1}=\sum_{i=1}^{n-1}(s_i-1)$.