Software cost estimation is an integral part of software development. Underestimated cost will most probable result low quality software. On the contrary, an overestimated one will cause resource wastages. This research has developed a model of software cost estimation using fuzzy logic. It also compares two COCOMOs estimation methods: Intermediate COCOMO and Fuzzy Intermediate COCOMO. The data used is NASA Projects done in between 1980 and 1990. The Models developed are evaluated using MRE (Magnitude of Relative Error), Mean MRE (MMRE), Median MRE (MdMRE), Min MRE, Max MRE, and Standard Deviation MRE (SdMRE). However, we only present MMRE to the readers, because it represents overall model performances. This experiment resulted MMREs of 59.50% for Intermediate COCOMO and 51.95% for Fuzzy Intermediate COCOMO. These results indicate that the fuzzy version of Intermediate COCOMO outperforms the non-fuzzy one. In addition, Fuzzy Intermediate COCOMO is sensitive to the values of Cost Drivers.