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In this paper, we develop a novel reduced-rank space-time adaptive processing (STAP) algorithm based on adaptive basis function approximation (ABFA) for airborne radar applications. The proposed algorithm employs the well-known framework of the side-lobe canceller (SLC) structure and consists of selected sets of basis functions that perform dimensionality reduction and an adaptive reduced-rank filter. Compared to traditional reduced-rank techniques, the proposed scheme works on an instantaneous basis, selecting the best suited set of basis functions at each instant to minimize the squared error. Furthermore, we derive stochastic gradient (SG) and recursive least squares (RLS) algorithm for efficiently implementing the proposed ABFA scheme. Simulations for a clutter-plus-jamming suppression application show that the proposed STAP algorithm outperforms the state-of-the-art reduced-rank schemes in convergence and tracking at significantly lower complexity.