Process mining is an analytical technique aimed at obtaining useful information about a process by extracting a process model from events log. However, most existing process models are deterministic because they do not include stochastic elements such as the occurrence probabilities or execution times of activities. Therefore, available information is limited, resulting in the limitations on analyzing and understanding the process. Furthermore, it is also important to develop an efficient methodology to discover the process model. Although genetic process mining algorithm is one of the methods that can handle data with noises, it has a limitation of large computation time when it is applied to data with large capacity. To resolve these issues, in this paper, we define a stochastic process tree and propose a tabu search-genetic process mining (TS-GPM) algorithm for a stochastic process tree. Specifically, we define a two-dimensional array as a chromosome to represent a stochastic process tree, fitness function, a procedure for generating stochastic process tree and a model trace as a string of activities generated from the process tree. Furthermore, by storing and comparing model traces with low fitness values in the tabu list, we can prevent duplicated searches for process trees with low fitness value being performed. In order to verify the performance of the proposed algorithm, we performed a numerical experiment by using two kinds of event log data used in the previous research. The results showed that the suggested TS-GPM algorithm outperformed the GPM algorithm in terms of fitness and computation time.