How can I avoid from turning mushrooms brown while freezing it?
One suggestion is to buy dried mushrooms and rehydrate them when you need them.  

As for freezing, as you probably know if you freeze them and thaw directly without any intervention you will probably get brown, mushy mushrooms.  There are a few ways to avoid this.

If you blanch the mushrooms first in some boiling water, then put them in an ice bath, that should stop the enzymes that cause the browning and also help with the texture some.  This method should also retain the most flavor of any of the preservation methods.

As a side note, I highly recommend going from freezer to cooking directly without thawing - this should reduce the amount of mushiness you will get.

I find that slicing and sauteing the mushrooms first in some oil or butter, then freezing them, works great for most uses, since sauteed is how I usually prefer my mushrooms anyway.  I just take them out of the freezer and throw them directly into the meal.

In my house the most common method is as I first mentioned, we buy dried portabellos etc and just rehydrate them into our meals.  However blanching and then freezing is often better for texture and taste, it just takes a little more time.

There are some great mushroom preservation methods available on this site.