Scheduling is important for improving performance in a distributed heterogeneous computing environment where workflows represented as a directed acyclic graph (DAG). The DAG task scheduling problem has been extensively studied, and many modern heuristic algorithms such as DONF and others have been proposed. Goal of this study is to propose an Artificial Neural Network (ANN) based scheduling scheme with Monte Carlo Tree Search (MCTS). Numerical representation of each DAG node are used as inputs to the ANN, and the outputs are the execution priority of the node. The MCTS method utilized to determine the actual scheduling policies; The proposed algorithm shows an improvement of up to 42% on certain graph topologies with average performance gain of 7.05% over the best scheduling algorithm. Algorithm managed to cover 40.01% of the proximity interval from the best scheduling algorithm to the global optimal solution obtained via the Mixed-Integer Linear Programming approach.