The technique of spectroscopy in astronomy is a research or a method which uses spectrum lines emitted by a body that emit electromagnetic ray. These lines will be used to determine the characteristics of any celestial body and one of the most dominant lines is H-α line. The research has been using 20RC Carbon Truss Ritchey-Chrétien telescope, SBIG Self Guided Spectrograph (SGS) with high resolution camera Couple-Charged Device CCD ST-7E. Since H-α line is to be found at 6562.817 Å, neon lamp is being used as calibration because of the obvious lines of this element is in the higher range of visible wavelength, from 5800 to 7500 Å. The software: TheSky and CCDSoft are being used for collecting and analyzing observed data while IRAF which being installed on LINUX interface are used to process the collected data. The data were processed to measure the full width half maximum (FHWM) and equivalent width (EW) for H-α line for each star. Seven M-type red giants that have been chosen are HD 80493, HD 148478, HD 39801, HD 112300, HD 101153, HD 156014 and HD 148783.