Recently a framework has been introduced within which a large number of classical and modern adaptive filter algorithms can be viewed as special cases. Variable Step-Size (VSS) normalized least mean square (VSSNLMS) and VSS Affine Projection Algorithms (VSSAPA) are two particular examples of the adaptive algorithms that can be covered by this generic adaptive filter. In this paper, we introduce a new VSS Partial Rank (VSSPR) adaptive algorithm based on the generic VSS adaptive filter and use it for channel equalization. The proposed algorithm performs very well in attenuating noise and inter-symbol interference (ISI) in comparison with the standard NLMS and the recently introduced AP algorithms.