The way used to estimate the fuzzy reliability differs according to the nature of the information of failure time which has been dealt in this research.The information of failure times has no probable distribution to explain it , in addition it has fuzzy quality.The research includes fuzzy reliability estimation of three periods ,the first one from 1986 to 2013,the second one from 2013 to 2033 while the third one from 2033 to 2066 .Four failure time have been chosen to identify the membership function of fuzzy trapezoid represented in the pervious years after taking in consideration the estimation of most researchers, proffional    geologists and the technician who is incharge of maintaining of Mosul Dam project. By using matlab programme , acpecial programme of research was designed to estimate the fuzzy reliability of last three periods ,according to the results it was found that fuzzy reliability of Al.mosul dam in the recent time reaches to 0.5 approxmatly  while the fuzzy reliability of Al.mosul dam after 20 years will reach to 0.1,ie, the danger of actual collapse of the dam will be in 2033 ,So that it is important to build a new dam making sure from chosing a suitable location with respect to soil quilty , geological and clamatic   which suround the location , This is to avoid the same mistake which makes us lose 33 years from the hypothetical life time of Mosul dam according to the estimation of the company which build the dam.