Moving Target Defense (MTD) has recently emerged as a game-changing technique in confronting cyber attacks and defending cloud computing systems (CCS) and computer networks (CN). A MTD technique randomly modifies the configurations of the attacked CCS, thus creating great uncertainties of the attack surface against cyber-intruders. In this paper, is proposed an analytical modeling approach based on the Matrix Stochastic Reward Nets (MSRN) with fuzzy parameters, that allows attacker’s behaviors compact modeling and analysis of the impact in which the use of a MTD technique influences the completion processing time of a running task by CCS. A numerical case study is presented to analyze the impact of different parameters on the expected task completion time and other evaluation metrics.