We tackle a 3D scene stylization problem - generating stylized images of a scene from arbitrary novel views given a set of images of the same scene and a reference image of the desired style as inputs. Direct solution of combining novel view synthesis and stylization approaches lead to results that are blurry or not consistent across different views. We propose a point cloud-based method for consistent 3D scene stylization. First, we construct the point cloud by back-projecting the image features to the 3D space. Second, we develop point cloud aggregation modules to gather the style information of the 3D scene, and then modulate the features in the point cloud with a linear transformation matrix. Finally, we project the transformed features to 2D space to obtain the novel views. Experimental results on two diverse datasets of real-world scenes validate that our method generates consistent stylized novel view synthesis results against other alternative approaches.