Manual scoring of sleep stages from polysomnography (PSG) records is essential to understand the sleep quality and architecture. Since the PSG requires specialized personnel, a lab environment, and uncomfortable sensors, non-contact sleep staging methods based on machine learning techniques have been investigated over the past years. In this study, we propose an attention-based bidirectional long short-term memory (Attention Bi-LSTM) model for automatic sleep stage scoring using an impulse-radio ultra-wideband (IR-UWB) radar which can remotely detect vital signs. Sixty-five young (30.0 ± 8.6 yrs.) and healthy volunteers underwent nocturnal PSG and IR-UWB radar measurement simultaneously; From 51 recordings, 26 were used for training, 8 for validation, and 17 for testing. Sixteen features including movement-, respiration-, and heart rate variability-related indices were extracted from the raw IR-UWB signals in each 30-s epoch. Sleep stage classification performances of Attention Bi-LSTM model with optimized hyperparameters were evaluated and compared with those of conventional LSTM networks for same test dataset. In the results, we achieved an accuracy of 82.6 ± 6.7% and a Cohen's kappa coefficient of 0.73 ± 0.11 in the classification of wake stage, REM sleep, light (N1+N2) sleep, and deep (N3) sleep which is significantly higher than the conventional LSTM networks (p < 0.01). Moreover, the classification performances were higher than those reported in comparative studies, demonstrating the effectiveness of the attention mechanism coupled with bi-LSTM networks for the sleep staging using cardiorespiratory signals.