The paper presents a cloud server roundtrip time prediction approach for cloud datacenters using neuro-fuzzy network with eight probability distribution functions (Normal, Rayleigh, Weibull, Gamma, Birnbaum-Saunders, Extreme Value, and Generalized Pareto) used for fuzzification and defuzzification. We predict the Round-Trip Time (RTT), i.e., the time for a network packet to travel from a client to a server and back. The proposed approach can achieve significant reduction in the short-time RTT prediction error, achieving an accuracy of 79.36%. The approach could be useful for increasing the efficiency of client-cloud systems, for example, when taking effective decisions for computational offloading, and contribute to the development of smart cloud computing.