Process discovery helps companies to automatically discover their existing business processes based on the huge, stored event log. The algorithms of process discovery have been developed rapidly to discover several types of relations, i.e., choice relations, non-free choice relations with invisible tasks. Invisible tasks in non-free choice, introduced by α $ method, is a type of relation that combines the non-free choice and the invisible task. α $ proposed rules of ordering relations of two activities for determining invisible tasks in non-free choice. The event log records sequences of activities, so the rules of α $ check the combination of invisible task within non-free choice. The checking processes is time consuming, and results in high computing times of α $. This research proposes Graph-based Invisible Task (GIT) method to discover efficiently invisible tasks in non-free choice. GIT method develops sequences of business activities as graphs and determines rules to discover invisible tasks in non-free choice based on relations of the graphs. The analysis of the graph relations by rules of GIT is more efficient than the iterative process of checking combined activities by α $. This research measures the time efficiency of storing the event log and discovering a process model to evaluate GIT algorithm. Storing a streaming event log in a graph-database has the lowest computing time than storing in other databases, i.e., SQL and MongoDB. Discovering a process model by GIT algorithm has less time complexity than that by α $, wherein GIT obtains O(n3) and α $ obtains O(n4) . In terms of computing time, GIT algorithm is 0.89 faster on batch event log and 0.85 seconds faster on streaming event log than α $. Those results of the evaluation show a significant improvement of GIT method in term of time efficiency.