Hi, I’m from HK. Please forgive for my poor English if you can’t really understand what I’m saying.
I’ve made a 3D model with some curve surface. I choose the smooth surface option and exported a .stl file. Finally the curve surface still shown as several rectangle. Did I do something wrong or it’s a limit on the free version sketchup?

You didn’t do anything wrong. The view is showing the faces that Sketchup uses to represent curved surfaces. Softening the edges in SketchUp won’t change the way they look in the print. You can make that less noticeable by using more segments in your curves. This may require you to model at a larger size. When I am modeling for 3D printing, I model with units set to meters. Many slicers will allow you to select the import units for the .stl file. If yours does, you can just export the .stl file but if yours doesn’t, you’ll need to scale the model down to the appropriate size before exporting.

Here’s a quick example. I modeled the bracket using many more than the default numbers of sides for the arcs and circles. The cylinder in the middle is modeled with the default 24-sided circle. The surfaces all look smooth in SketchUp.

I’ve try to create the model in a larger size. But I found that all the curves are fixed composing by 12 faces even it’s a half ,1/4 or 1/8 circle.
I’ll use the exported file for 3D rendering by Adobe Dimension. Does it mean that I can’t make a really smooth curves surface by Sketchup?

This is what I mean all curves composed by 12 faces

Before you draw the arcs, increase the number of sides. Pay attention to the Measurements window when you get the Arc tool. After you select the tool it will show 12 sides. You can change that to a larger number. Keep in mind there’s little if any benefit to using extremely large numbers. Probably something like 48 will be enough. You can’t change the number of sides once you have your model 3D as you show in your screen shot.

Curves in SketchUp will always be made of straight line segments and curved surfaces will always be made of flat faces. As I showed earlier, you can make the surfaces look smoother by using more sides when you draw the curves.

Oh! I found it.
Although I still can’t add more sides since the “+” can’t directly typed in Mac pro. But I think I get the way. I’ve get more try. Thanks!