A novel vector-space-based adaptive filtering (VAF) algorithm for acoustic echo cancellation (AEC) is presented. The proposed VAF algorithm can be divided into two phases: offline and online. In the offline phase, VAF constructs a vector space to incorporate the prior knowledge of adaptive filter coefficients from a wide range of different channel characteristics. Then, in the online phase, a mapping function is derived to estimate the adaptive filter for the testing condition using the constructed vector space. By using the vector space, VAF can effectively and efficiently estimate the parameters of the adaptive filter for the unknown testing condition. The experimental results for three designed AEC tasks demonstrate that VAF provides notably faster convergence rates compared to conventional adaptive filtering methods.