I downloaded the org.Hs.eg.db_3.1.2.tar.gz package, when I wanted to install it using install button in R and browse the file after while I saw:

* installing *source* package ‘org.Hs.eg.db’ ...
** R
** inst
** preparing package for lazy loading
Error : package ‘AnnotationDbi’ 1.28.2 was found, but >= 1.29.20 is required by ‘org.Hs.eg.db’
ERROR: lazy loading failed for package ‘org.Hs.eg.db’
* removing ‘/Library/Frameworks/R.framework/Versions/3.1/Resources/library/org.Hs.eg.db’
Warning message:
In install.packages("~/Desktop/org.Hs.eg.db_3.1.2.tar.gz", repos = NULL,  :
  installation of package ‘/Users/tina/Desktop/org.Hs.eg.db_3.1.2.tar.gz’ had non-zero exit status

for highlighted error I tried to install new version of AnnotationDbi using

biocLite("AnnotationDbi")

but it installed version 1.28.2 like before. Anyone can help me?

Upgrade to R 3.2.0 (current release version). Then biocLite() will provide the correct versions. Using biocLite() is the recommended way to end up with the correct versions; downloading package archives will result in problems like you have experienced.