The necklace hypercube network has recently been introduced as an attractive alternative to the well-known hypercube. Previous research on this network topology has mainly focused on topological properties and VLSI aspects of this network. In this paper, we propose some adaptive routing algorithm for the necklace hypercubes. The performance of necklace hypercubes using the proposed routing algorithm is then evaluated by means of simulation experiments. Experiments are realized under different working loads and for different network factors. Moreover, a comparison between the necklace hypercube and the well-known hypercube network is conducted. The comparison has been done considering implementation constraints including constant pin-out and constant bisection band-width constraints.