Estimating the cost of software is a complex process for almost all engineering companies. Uncertainties about development method, design, estimation process, data, and processing affect the accuracy of estimation. Underestimation results in fewer resources being committed than the project really needs, an unrealistic schedule, and low quality outputs. On the other hand, overestimation wastes resources and causes loss of customer credit. Thus, choosing the appropriate cost estimation method is crucial. Studies in the literature emphasize the importance of empirical, analytical methods and expert judgement. Certain cost estimation techniques have been widely studied in the literature. However, there are limited studies using fuzzy approaches for software cost estimation. This paper presents a hesitant fuzzy pairwise comparison (HFPC) used in the hesitant fuzzy analytic hierarchy process for software cost estimation problems by using expert judgement. For this purpose, first a number of criteria are selected with the help of expert judgements from the Turkish banking sector and information technology industry. Subsequently, the HFPC method is presented to estimate the cost of software projects. In order to analyze the efficiency of the proposed approach, it is applied to a software cost estimation problem for a Turkish company. It is seen that the proposed method provides efficient estimations due to low deviation between the real effort and estimated cost. The results are also approved by experts working in the relevant software company.