Glottal closure instants (GCI) are the instants of significant excitation of the vocal tract system during the production of speech. The performance of many speech analysis and synthesis approaches depends on accurate estimation of GCIs. A new method for detection of GCI locations in speech utterances using Fourier-Bessel (FB) expansion and amplitude and frequency modulated (AM-FM) signal model is proposed in this paper. The inherent filtering property of the FB expansion is used to weaken the effect of formants in the speech utterances. The band-limited signal reconstructed using FB coefficients has been considered as an AM-FM signal. The discrete-energy separation algorithm (DESA) has been used to estimate the amplitude envelope (AE) function of the AM-FM signal model. The estimated AE function is explored for detection of GCIs. The CMU-Arctic database is used in this work for the validation of the proposed method for GCI detection with the electro-glottograph (EGG) as a reference. It has been observed that the detected GCI by the proposed method seems to provide accurate location of GCIs.