Energy storage technologies (ESTs) enable to cope with intermittency of energy sources by storing excess energy to use when it is needed. Therefore, evaluation of energy storage alternatives (or technologies) is completely critical and can be exactly considered as a multi-criteria decision making (MCDM) problem. It is clear that we have to evaluate this problem in terms of both qualitative and quantitative criteria. We should also take into account decision makers' linguistic evaluations and their experiences. At this point, the fuzzy set theory (FST) that is an effective tool to utilize from human judgments and linguistic evaluations in the decision making process can be successfully used. Hesitant fuzzy sets (HFSs) that enable to have several membership values between 0 and 1 for an element of the set can be used for this aim as an extension of ordinary fuzzy sets. In this paper, an integrated MCDM model consists of Delphi, Analytic Hierarchy Process (AHP) and VIsekriterijumska Optimizcija I Kompromisno Resenje (VIKOR) methods has been proposed to evaluate EST alternatives for Turkey under hesitant fuzzy environment. For this aim, a hierarchical decision model consisting of four main criteria and nineteen sub-criteria with nine EST alternatives has been constructed. While hesitant fuzzy AHP (HF-AHP) method has been utilized to determine weights of criteria, the alternatives have been ranked by using hesitant fuzzy VIKOR (HF-VIKOR) method. A sensitivity analysis based on change of some parameters has been also performed to analyze the obtained results and to demonstrate sensitiveness of the proposed MCDM model. A comparative analysis has been also realized to confirm the validity of the proposed fuzzy based methodology. For this aim, hesitant fuzzy Technique for Order Preference by Similarity to Ideal Solution (HF-TOPSIS) method has been applied as another distance-based methodology. One of the obtained results of this study is that the criteria economic and technical have been determined as the most and the least important main criteria and the weights of them have been achieved as 0.342 and 0.203, respectively. Additionally, the alternative EST named "Compressed Air" has been determined as the most suitable energy storage technology alternative for Turkey.