Is there a browser on android accepting extensions?

You can try Firefox for Android. You can write extensions for it.

There are not many mobile browsers supporting extension.

Indeed, I have been interested in this question for the last year and I only found Dolphin (as @vvieux wrote) supporting add-ons and other cool features announced few days ago. Firefox Mobile ones look very "simple" for me.

The Dolphin API can be found here with two different approaches as you can see:

• Add-on (quite simple):

  A Dolphin Add-on is an Android application that interacts with the Dolphin browser to create new functionality. An Add-on can interact with web pages or with browser features such as bookmarks, history, and tabs.

• Web App accessing "native" features:

  Dolphin gives developers the option of publishing an app, not as a package, but as a thin-client web app for Dolphin users.

As a personal note: I hope to go with the second ones soon.

Russian company has released Yandex Browser Alpha, based on Chromium, and it accepts desktop Chrome extensions. Opera addons also should work.

Also FireFox for Android supports WebExtensions, which are somewhat compatible with Chrome extensions API.