We analyzed the carotid artery blood flow waveform (CABFW) through multivariate autoregressive analysis in a case with multicystic encephalomalacia (MCE) after neonatal asphyxia and compared the result with those of 35 healthy newborns. The total power of CABFW was at the -2 SD level of the value for 35 healthy newborns, and the power, % power, bio-informing amounts and damping time of component 3 (damping frequency 11.15 Hz) were less than -2 SD of the values in 35 healthy newborns. The Pulsatility Index (PI) of anterior cerebral artery (ACA) was high (0.76). These results suggest that cerebral blood flow decreases because of cerebral vasoconstriction in MCE after neonatal asphyxia.