I was wondering if there is for korean language a web site similar to the following made for japanese language:
They are both a reference for grammar and writing system.
KoreanClass101.com has a "grammar bank" (paywalled; check it out with a free 7-day trial):
The Grammar Bank is a one-stop collection of detailed write-ups covering over one hundred Korean grammar constructions. Learn the basic formation, read sample sentences, and study notes that cover the small details that really help you master the construction of the language.
Due to the paywall, I can't comment on the quality of the grammar bank, but I was pretty impressed with their lessons on Korean pronunciation (one audio series and one video series; both were the best I've found online.)
howtostudykorean.com is probably your best bet (as topo morto already commented)