Attenuation of alpha wave is considered as the most valid marker of sleep onset during sleep, but this has received little attention during driving. Interestingly, from our simulated driving experiments, a new alpha wave's attenuation-disappearance phenomenon was observed to frequently appear in eye closure events (ECEs), with an obvious split point, which divides ECE into alpha attenuation phase and alpha disappearance phase. Firstly, we used box plots to visualize the general distribution of the alpha wave's power spectrum density (PSD) values in each of the two phases. Secondly, more quantitative analysis method was used to examine the characteristics of change in alpha PSD values. In addition, we analyzed the duration distribution of ECEs with alpha attenuation-disappearance phenomenon to measure sleepiness level and calculated the percentage of these ECEs across four sub duration ranges. The experimental results indicate that there is a general sharp decline of alpha PSD values from the alpha attenuation phase to the alpha disappearance phase among all the ten subjects. This result is consistent with visual observations and verified the alpha wave's attenuation-disappearance phenomenon as a general pattern. Moreover, this alpha attenuation pattern was proved to be more likely to appear under the condition of higher sleepiness level, predicting the entry into sleep.