This paper proposes a fast search algorithm for vector quantization (VQ) based on a binary search space (BSS-VQ). The trade-off and learning aspects (TLA) were used to enhance the line spectrum pair (LSP) encoder of the G.729 standard. In the trade-off aspect, a slight loss occurred in the quantization quality; however, substantial computational savings were achieved. In the learning aspect, the binary search space was developed using he learning process, which uses full search VQ (FSVQ) as an inferred function. In the experiment, computational savings of 86.19% and a quantization accuracy of 98.15% were achieved, which confirmed the excellent performance of the BSS-VQ approach.