Recent research on the time-domain audio separation networks (Tas-Nets) has brought great success to speech separation. Nevertheless, conventional TasNets struggle to satisfy the memory and latency constraints in industrial applications. In this regard, we design a low-cost high-performance architecture, namely, globally attentive locally recurrent (GALR) network. Alike the dual-path RNN (DPRNN), we first split a feature sequence into 2D segments and then process the sequence along both the intra-and inter-segment dimensions. Our main innovation lies in that, on top of features recurrently processed along the inter-segment dimensions, GALR applies a self-attention mechanism to the sequence along the inter-segment dimension, which aggregates context-aware information and also enables parallelization. Our experiments suggest that GALR is a notably more effective network than the prior work. On one hand, with only 1.5M parameters, it has achieved comparable separation performance at a much lower cost with 36.1% less runtime memory and 49.4% fewer computational operations, relative to the DPRNN. On the other hand, in a comparable model size with DPRNN, GALR has consistently outperformed DPRNN in three datasets, in particular, with a substantial margin of 2.4dB absolute improvement of SI-SNRi in the benchmark WSJ0-2mix task.