I did a search in google and found this formula that's supposed to work:
(Please see the following)

To count dates within a range (inclusive):

B1 = start date = 1/1/2006
C1 = end date = 7/1/2006

=COUNTIF(A1:A10,">="&B1)-COUNTIF(A1:A10,">"&C1)

Then it should be:

=COUNTIF(A1:A10,">="&1/1/2006)-COUNTIF(A1:A10,">"&7/1/2006)

But this only counts the number of cells that has the date, but not based on the range, why it doesn't work??