Introduced by Du and Liu in 2007, a (k, m)-ary tree is a generalization of k-ary tree such that the nodes have degree k on even levels and the nodes have degree 0 or m on odd levels. Especially, every node with the degree m on odd levels is called a crucial node. In a (k, m)-ary tree of order n, there are exactly n crucial nodes. A loopless algorithm is an algorithm for generating combinatorial objects using only assignment and comparison statements and does not include loop structure or recursion. In this paper, we propose a loopless algorithm to generate (k, m)-ary trees of order n in Gray-code order using Z-sequence suggested by Zaks in 1980. The required memory space of our algorithm is \(2n+\mathcal {O}(1)\). Moreover, we analyze both amortized costs of assignment statements and comparison statements, which are no more than \(3+\frac{3}{km}\) and \(2.5+\frac{2}{km}\), respectively.