In this work, we propose a novel low-complexity reduced-rank scheme and consider its application to linear interference suppression in direct-sequence ultra-wideband (DS-UWB) systems. Firstly, we investigate a generic reduced-rank scheme that jointly optimizes a projection vector and a reduced-rank filter by using the minimum mean-squared error (MMSE) criterion. Then a low-complexity scheme, denoted switched approximation of adaptive basis functions (SAABF), is proposed. The SAABF scheme is an extension of the generic scheme, in which the complexity reduction is achieved by using a multi-branch framework to simplify the structure of the projection vector. Adaptive implementations for the SAABF scheme are developed by using least-mean squares (LMS) and recursive least-squares (RLS) algorithms. We also develop algorithms for selecting the branch number and the model order of the SAABF scheme. Simulations show that in the scenarios with severe inter-symbol interference (ISI) and multiple access interference (MAI), the proposed SAABF scheme has fast convergence and remarkable interference suppression performance with low complexity.