A contractor removed our old thermostat during remodeling and installed a White-Rodgers thermostat after remodeling. When I turned on the power of the central air, the furnace transformer was blown. It happened twice. Here are some images
http://imgur.com/FlcLl,xQpvy,o0zeq#2
http://imgur.com/FlcLl,xQpvy,o0zeq
http://imgur.com/FlcLl,xQpvy,o0zeq#1
Before the thermostat change, the old system worked fine.
Is it caused by a bad connection or something else?

Your pics didn't show up. Please try again. It could be that the stat is wired incorrectly (most likely is the problem). Or it could be a couple other things. Lets start with the stat wiring and go from there. I will need to know exactly where the stat wires are hooked to in the furnace to be able to tell you where they need to go on the stat.

Here are images I captured. Besides the thermostat, we also upgraded the electrical panel during the remodeling.
I just measured the failed transformer. The 120V side was damaged.
http://www.flickr.com/photos/9875895...in/photostream
http://www.flickr.com/photos/9875895...in/photostream
http://www.flickr.com/photos/9875895...in/photostream

The website has a little problem to process image links. I give these image links directly.
thermostat | Flickr - Photo Sharing!
furnace | Flickr - Photo Sharing!
furnacemodel | Flickr - Photo Sharing!

Thanks

So did replacing the transformer solve the problem? You need to disconnect the black wire from the o terminal on the thermostat. It looks like the black wire is hooked from the o on the stat to the c on the furnace control board. If you can either unhook it from the c at furnace, or from o at stat. Or better yet, disconnect it at both locations. C stands for common, and your stat doesn't have a common terminal. Having the common hooked to the o on stat could very well cause your transformer problem when switched to a/c. Disconnect this wire and let me know how things turn out. Should solve your problem. Also, I would sugget installing a three amp inline fuse on the hot wire of the 24v side of the transformer to protect the new trans from this type of thing in the future. Good luck and please do keep us posted.

Thanks for your guide.
Our region gets colder recently. Will follow your guide when the weather gets a little warmer and post the result.