Nowadays, Computational Fluid Dynamics (CFD) simulations play an increasingly important role for turbine airfoil design. This high-fidelity approach is capable to provide accurate information of flow fields. Meanwhile, the calculation accuracy is always gained at the expense of numerical cost. This gap limits opportunities for design space exploration. To address this problem, surrogate models (also known as metamodels) are introduced to approximate high-fidelity CFD models. However, traditional surrogate models, such as Kriging or Radial Basis Function, construct response surface on a design space with limited dimensions. This prevents users from predicting the flow fields directly from the geometry and performing interactive design of airfoil. In the present work, we propose a Convolutional Neural Network (CNN) based surrogate model to predict flow properties on turbine vane airfoil surface from 3D airfoil profile defined by point cloud. The proposed CNN architecture adopts a symmetric expanding path that is similar to the so-called U-Net. The geometries in the training and testing dataset are generated via varying the parameters defined by the Free-Form Deformation approach. The corresponding flow fields are obtained through high-fidelity CFD simulations performed in a finite volume context. Furthermore, a gaussian process based Bayesian optimization technique is utilized to tune automatically the hyperparameters of the network. In this work, we trained the CNN based surrogate model with static pressure and temperature on the mean section of turbine vane airfoil surface. The trained model is able to predict in a reliable and efficient way the corresponding property directly from the 3D geometry, which allows engineers to agilely adjust their airfoil design.