Software cost estimation is the process of predicting the effort required to develop a software system. The objective of this paper is to examine the application of applying fuzzy logic in software cost estimation & obtain more accurate result. This paper proposes an adaptive software cost estimation model incorporates fuzzy logic technique to handle imprecision and uncertainty of software attributes. Here, using FL-COCOMO II model produced better estimation accuracy than the COCOMO II model. The evaluation of the obtained results, using Mean of Magnitude of Relative Error (MMRE) and PRED evaluation techniques, showed that the FL-COCOMO II produced the MMRE less than the original COCOMO and the value of PRED in the Fuzzy-COCOMO II is higher than the original COCOMO. Furthermore, the FL-COCOMO II provides better improvement in terms of estimation accuracy using MMRE when compared with the original COCOMO. This model incorporates fuzzy logic technique to handle imprecision and uncertainty of software attributes & improve the accuracy of software estimates.