The differentiation between the openness and other dimensions of the Big Five personality model indicates that it is necessary to design a specific paradigm as a supplement to the Big Five recognition. The present study examined the relationship between one's openness trait of the Big Five model and the task-related power change of upper alpha band (10–12 Hz). We found that individuals from the high openness group displayed a stronger alpha synchronization over a frontal area in symbolic reasoning task, while the reverse applied in the deductive reasoning task. The results indicated that these two kinds of reasoning tasks could be used as supplement of the Big Five recognition. Besides, we divided one's openness score into three levels and proposed a hybrid-SNN (Spiking Neural Networks)-ANN (Analog Neural Networks) architecture based on EEGNet to recognize one's openness level, named Spike-EEGNet. The recognition accuracy of the two tasks was 90.6 and 92.2%. This result was highly significant for the validation of using a model with hybrid-SNN-ANN architecture for EEG-based openness trait recognition.