In the competitive electric power market allowing open access transmission environment, the knowledge of available transfer capability (ATC) is very important for optimum utilization of existing transmission facility. ATC information conveys how much power can be transmitted through the power network over and above already committed usage without violation of system security limits. This paper presents a Levenberg-Marquardt algorithm neural network (LMANN)-based approach for fast and accurate estimation of system ATC. System ATC has been estimated for both varying load condition as well as for single line outage contingency condition by employing distributed computing. Principal component analysis (PCA) has been applied for effective input feature selection. Contingency clusters are formed such that each cluster contains almost similar ATC values. For each contingency clusters separate LMANNs have been developed. All the proposed LMANNs have been trained and tested under distributed computing environment and a considerable speed up in the training is obtained. The proposed approach has been examined on 75-bus Indian power system and IEEE 300-bus system and found significantly efficient.