Process discovery is a concern in analyzing business processes. Process discovery methods handle many aspects, e.g. a hybrid of non-free choice and invisible task. A hybrid of non-free choice and an invisible task is a condition that needs additions of invisible tasks in non-free choice relationships. Process discovery methods, e.g. Alpha++, Alpha#, Graphical method, Time-based Alpha Miner, cannot discover the hybrid of non-free choice and invisible task, especially invisible tasks in the overlapping pattern. To modeling a hybrid of non-free choice and invisible tasks, this research proposes an algorithm of adding invisible tasks, including invisible tasks of overlapping pattern, automatically in the event log and processing the event log with the rules of Alpha++ algorithm. To test the proposed algorithm, namely Invisible Task Log with Alpha++, the experiment compares it with Alpha++, Alpha#, Graphical Method, Time-based Alpha Miner, Hidden Markov Model-Parallel, and Coupled Hidden Markov Model-Invisible Task. The experiment results proved that Invisible Task Log with Alpha++ algorithm obtains higher precision than the obtained precision by comparison methods.