  The theory of almost characters which is closely related to character sheaves
is proposed by Lusztig to study the representation theory of finite reductive
groups. In this article we show that the decomposition of the Weil character
for finite reductive dual pairs $(\Sp_{2n},\rmO^\pm_{2n'})$ or
$(\Sp_{2n},\SO_{2n'+1})$ with respect to the almost characters is exactly the
same as the decomposition with respect to the irreducible characters. As a
consequence, the finite theta correspondence on almost characters is
established.
