We theoretically study the electron detachment of negative hydrogen ions in a three-cycle linearly polarized laser field with a wavelength of 2150 nm in the context of the strong field approximation (SFA). The numerical integration and the saddle-point (SP) methods are both used in our calculations. The results show that both the energy spectra and the momentum spectra of the photoelectrons detached from negative hydrogen ions, obtained from these two methods, accord very well with each other for the laser intensities of 1.31011 W/cm2 and 6.51011 W/cm2, respectively. It is found that there is an obvious stripe-like structure along the vertical direction of the momentum spectra when the laser intensity is 6.51011 W/cm2. To explore the main origin which leads to the specific structures of the momentum spectra, we divide the interferences of the electronic wave packets emitted at different times during the laser pulse into the intra-cycle interference and the inter-cycle interference based on the SP method. Inter-cycle interference arises from the coherent superposition of electron wave packets released at complex times during different optical cycles, whereas intra-cycle interference comes from the coherent superposition of electron packets released in the same optical cycle. It is found that when only considering the inter-cycle interference, the main structures of the momentum spectra accord well with the above-threshold detachment (ATD) rings, which indicates that the inter-cycle interference corresponds to ATD rings of the photoelectron spectrum. But when only considering the intra-cycle interference, there are stripe-like structures with left-right asymmetry along the vertical direction of the momentum spectra. So the main structures of the momentum spectra of the photoelectrons are attributed to the interplay of the intra-and inter-cycle interferences. In addition, to intuitively explain the reason why the momentum spectra depend on the intensity of the laser field, we analyze the influence of the intensity of the laser field on the inter-cycle interference of quantum wave packets. It is found that the phase difference of the inter-cycle interference depends on the intensity of the laser field, which may lead to the difference among the momentum spectra of the photoelectrons at different laser intensities. Moreover, the influences of the intra-and inter-cycle interferences on the energy spectrum of the photoelectrons are also analyzed. It is found that the main oscillatory patterns and the peak positions of the energy spectra are mainly determined by the inter-cycle interference. Finally, the effects of the duration of laser pulse on the intra-and inter-cycle interferences are discussed. It seems that the main structures of the momentum spectra accord well with the ATD rings in multi-cycle laser pulses. So it is concluded that in multi-cycle laser pulses, the inter-cycle interference dominates while the intra-cycle interference is suppressed. The work in this paper is meaningful for further understanding the quantum interference effect and the optical control of the laser-induced photodetachment of negative ions.