Neural development of infants has drawn increasing research interests from the community. In this paper, we investigated the frequency band power of 112 infants who participated in an auditory oddball experiment, and the visual expectation (VE) score of 177 infants who went through a visual expectation paradigm test. Analysis found that the frequency band power decreases in the delta and theta bands, and increases in the alpha and beta bands when the infants grow up from 6 months old to 18 months old. We also proposed a sustainability index to measure the capability of a subject to maintain their band power in the auditory oddball experiment when infants grow up from 6 months old to 18 months old. Analysis shows that the sustainability index increased significantly in the alpha and beta band, decreased in the delta and theta bands. Correlation between the VE score and frequency band power was investigated on 47 infants who participated in both auditory oddball experiment and visual expectation paradigm test. Analysis shows that the reaction speed to stimulus have statistical a significant correlation with the changes of band power and sustainability index in posterior and temporal section, and in the higher frequency bands.