Oscillations generated by dynamic interactions between power electronics and grid are becoming one of the intractable issues in renewable powered systems. To know the stability region of oscillations is important for the evaluation of oscillation risk in a practical power system. Conventionally, oscillatory stability region is constructed using pointwise method, which has disadvantages in computational efficiency. To fill this gap, this paper proposes a novel approach to the stability region construction using a random forest classifier. Firstly, an oscillation stability analysis program is developed to obtain stability datasets for a power system with different parameters. Then the max-relevance and min-redundancy (mRMR) method is utilized to select critical features for the adoption of random forest. Finally, the oscillatory stability region is identified with random forest based on the selected critical feature. Validity of the method is validated using a grid-connected voltage source converter (VSC) system.