Based on the algebraic degree and the algebraic thickness of Boolean functions

the relationship of algebraic thickness between a Boolean function and their decomposing Boolean functions is given

and the upper bound on the algebraic thickness of Boolean functions with

n

variables is 2* *(

n

-1) by the recurrence method and the reduction to absurdity.The upper bound answers the open problem:"whether there exists a Boolean function with

n

variables whose algebraic thickness is strictly greater than 2* *(

n

-1)".At the end of this paper

according to this fact an upper bound on algebraic thickness of elementary symmetric Boolean functions of

n

variables with algebraic degree

k

(2≤

k

≤(

n

-1)/2) is improved

and some properties on algebraic thickness of Boolean functions are derived.