Sorry for my bad English.

The internet speed where I live right now is pretty poor(<0.1Mbs).

It is impossible for me to finish downloading the 17G patch.

So I downloaded the 4 parts of patch 1.10 installer in the place with better internet speed and brought it to my computer.

After I finished installing it and logged in the galaxy, it showed that it is still patch 1.08 and started to download the 17G patch.

But in the game it already shows that it is patch 1.10.

Is there any way to fix it?

You could try this: Deinstall Galaxy and install it again. Import Witcher 3 to Galaxy and hope it will recognize this time that Witcher 3 is version 1.10 now.

== IMPORT ALREADY INSTALLED GAMES TO GALAXY ==

1. For GOG games installed using installers from the last few months (so called Galaxy-compatible installers)
Click the "+" button on top of the sidebar and select "scan and import folders" - it will find all compatible games within that folder and add them to the Client.

2. For remaining GOG game INSTALLATIONS
Find the game in the Library (click on the image of the game), then click the More button and select "Manage" -> "Import folder" and point the folder selector into the folder where that game is installed.
Please be aware that Client will accept any folder pointed to and will overwrite files inside it (this can for example wipe some mods or damage other apps in case of pointing to a wrong folder) and will update the game to the newest version (current default language English).
Source: http://www.gog.com/forum/general/gog_galaxy_beta_2/post1

This works. See here:
http://www.gog.com/forum/the_witcher_3_wild_hunt/gog_galaxy_patch_version_not_match_with_the_game_version