Naked eye observations at Tubruq sky (φ = 32° 05´, λ = 23° 59´) in Libya at the Mediterranean coast (see-desert background) during the two years (2008 – 2009) of morning twilight have been recorded.  These observations led us to get some estimates about morning twilight, as it is necessary to determine the time of the True Dawn (Al-Fajr Prayer Time).  this research aims to determine the correct time of Al-Fajr Prayer by finding the accurate angle of the sun vertical depression below the horizon that is associated with legitimate mark. The Methode used in this research was field research while the observations have been recorded by monitoring the first white thread on the eastern horizon (True Dawn) that announces the time of the Morning Prayer (Al-Fajr Prayer).  The azimuthally range of observation about the solar vertical extends from 0° up to ±20°, while the phenomenon was followed from 0° up to 20° along the altitudinal range.  This research gives a result that a beginning of the morning twilight is estimated to be around 13.5° depression of the sun below the horizon.  This value can reach a minimum depression around 11.5° at low visibility and a maximum around 13.5° at a very god visibility.