Everyday information systems collect a different kind of process instances of a business flow. As time goes on, the size of the collected data builds up speedily and constitutes a huge amount of data. It is a very challenging task to obtain valuable information and features of processes from such big data. Considering in advance, the trend and different features of the ongoing process are essential. Especially, time management is crucial in designing and conducting business processes. In this article, a novel process miner algorithm is proposed for time prediction, named time-oriented İnteractive process miner (T-IPM), which predicts the remaining and completion time of each process in a business workflow. The goal is to develop a process miner algorithm for time prediction that is able to work on a huge amount of event logs, and to incorporate the execution records of ongoing processes into the discovered process model instantly. In this study, three datasets from different domains that include event logs of repair, hospital, and traffic process flows were used to carry out the experimental studies in order to show the effectiveness of the proposed time prediction algorithm. The experimental studies show that the proposed algorithm is capable of performing process analysis on a huge amount of event logs with low memory consumption and high prediction accuracy.