Deep neural networks have shown excellent prospects in speech separation tasks. However, obtaining good results while keeping a low model complexity remains challenging in real-world applications. In this paper, we provide a bio-inspired efficient encoder-decoder architecture by mimicking the brain's top-down attention, called TDANet, with decreased model complexity without sacrificing performance. The top-down attention in TDANet is extracted by the global attention (GA) module and the cascaded local attention (LA) layers. The GA module takes multi-scale acoustic features as input to extract global attention signal, which then modulates features of different scales by direct top-down connections. The LA layers use features of adjacent layers as input to extract the local attention signal, which is used to modulate the lateral input in a top-down manner. On three benchmark datasets, TDANet consistently achieved competitive separation performance to previous state-of-the-art (SOTA) methods with higher efficiency. Specifically, TDANet's multiply-accumulate operations (MACs) are only 5\% of Sepformer, one of the previous SOTA models, and CPU inference time is only 10\% of Sepformer. In addition, a large-size version of TDANet obtained SOTA results on three datasets, with MACs still only 10\% of Sepformer and the CPU inference time only 24\% of Sepformer.