Hello. Check out this website http://www.morim.com/cour_notion.php There is a lot of free material for different levels. Kind regards

Thank you very much, Lydia! Of course, I read Tanakh. I listen Hebrew singers too (Ofra Haza, Eyal Golan, Sarit Hadad etc.). Also I read fairy tails in Hebrew. And I think that site that you recommend me will be helpful too. Toda raba!

http://www.hebrew4christians.com/Grammar/grammar.html This is the website where I learned to read. I've been told I read well. As you click on the 'vowels', you will find there are various pronunciation exercises where you can play the voice and check yourselves. This really helped me. There are other helpful resources for you to advance in reading also if you go to this website's store and go to Hebrew Audio Products. I regularly listen to the Bible in Hebrew and read it at the same time, this teaches me proper pronunciation. The narrated Bible they have on this website is absolutely excellent, but he reads at natural speed. If you want something at slower speed you can get "Reading the Bible in Hebrew", where he reads at a slower speed as well. And you can find the text online, there are many websites.

Thank you very much, Chackomatic! Your link is very helpful, I didn't know it. As for 'Rosetta Stone', I have that program and I use it. Anyway thanks!

Biblical Hebrew is very different from the modern dialect by vocabulary and sentence structure... Most Israelis can understand the biblical form without a real difficulty but nobody speak it in a daily manner... Still it has the same alphabet. I think that the Rosetta Stone method is the closest to the method your looking for...MA MU ME at least the reading part ( and you can download a cracked version of it )