The accurate cost estimation of a construction project in the early stage plays a very important role in successfully completing the project. In the initial stage of construction, when the information necessary to predict construction cost is insufficient, a machine learning model using past data can be an alternative. We suggest a two-level stacking heterogeneous ensemble algorithm combining RF, SVM and CatBoosting. In the step of training the base learner, the optimal hyperparameter values of the base learners were determined using Bayesian optimization with cross-validation. Cost information data disclosed by the Public Procurement Service in South Korea are used to evaluate ML algorithms and the proposed stacking-based ensemble model. According to the analysis results, the two-level stacking ensemble model showed better performance than the individual ensemble models.