The hypercube-like networks are a class of important generalization of the popular hypercube interconnection networks for parallel computing. This paper is concerned with the fault-tolerant cycle embedding ability of a subclass of hypercube-like networks, called restricted hypercube-like networks (RHLNs, for short), which include most of the well-known hypercube variants, such as the twisted cubes, the crossed cubes, the locally twisted cubes, and the Mobius cubes. We show that for n >= 5 and f <= 2n - 7, a fault-free cycle of length at least 2n - f - (n - 5) can be embedded in an n-dimensional RHLN with f faulty nodes. Our work extends the previous known result in the sense of maximum number of faulty nodes tolerable in an RHLN.