Parallel and distributed systems have seen significant development and application in areas such as big data processing, cloud computing, edge computing, deep learning, and artificial intelligence. The network architecture serves as a crucial component in parallel and distributed systems. Circulant-based recursive networks (CRNs), one kind of networks, include well-known networks such as the interconnection network hypercube, the k-ary n-cube network, and the data center network BCube, as well as some less-known networks. In this paper, we design an O(lk) algorithm, named DJ-Path1, to construct \(l(k+1)\) disjoint paths between any two adjacent vertices in k-dimensional n-order CRN with the maximum length being \(l+n-2\) . Additionally, we propose another \(O(kl(k+l))\) algorithm, called DJ-Path2, to construct \(l(k+1)\) disjoint paths between any two nonadjacent vertices with the maximum length being \(\langle \lceil \frac{n-1}{l} \rangle \rceil k+(n-l+2)\) , where l denotes the degree of the 0-dimensional n-order CRN.