In this paper, a phase spectrum based acoustic parameter is presented for the detection of nasalized vowels from the mixture of oral and nasalized vowels of normal speakers. Acoustic analysis shows that during the event of nasalization, although additional formants (resonances) at various frequency locations are introduced, the introduction of a new formant in low frequency region around 250 Hz is found to remain consistent irrespective of female or male speakers in the modified group delay derived from the phase spectrum. By exploiting and verifying this fact on the band-limited modified group delay spectrum capable of resolving two closely spaced formants, an acoustic parameter RMGD is derived. Utilizing RMGD, the problem of detecting nasalized vowels is solved based on a threshold based scheme or a Euclidean distance based classifier. Simulation Results on TIMIT database show that the proposed method even with a simple classifier is superior in performance in comparison to that of the methods using Mel-frequency cepstral coefficients as a feature and Hidden Markov Modeling or Support Vector Machine as a classifier.