Motor imagery (MI), an important category in electroencephalogram (EEG) research, often intersects with scenarios demanding low energy consumption, such as portable medical devices and isolated environment operations. Traditional deep learning (DL) algorithms, despite their effectiveness, are characterized by significant computational demands accompanied by high energy usage. As an alternative, spiking neural networks (SNNs), inspired by the biological functions of the brain, emerge as a promising energy-efficient solution. However, SNNs typically exhibit lower accuracy than their counterpart convolutional neural networks (CNNs). Although attention mechanisms successfully increase network accuracy by focusing on relevant features, their integration in the SNN framework remains an open question. In this work, we combine the SNN and the attention mechanisms for the EEG classification, aiming to improve precision and reduce energy consumption. To this end, we first propose a noniterative leaky integrate-and-fire (NiLIF) neuron model, overcoming the gradient issues in traditional SNNs that use iterative LIF neurons for long time steps. Then, we introduce the sequence-based attention mechanisms to refine the feature map. We evaluated the proposed noniterative SNN with attention (NiSNN-A) model on two MI EEG datasets, OpenBMI and BCIC IV 2a. Experimental results demonstrate that: 1) our model outperforms other SNN models by achieving higher accuracy and 2) our model increases energy efficiency compared with the counterpart CNN models (i.e., by 2.13 times) while maintaining comparable accuracy.