Since the symmetry axis equation of $y=\cos x$ is $x=k\pi$, where $k\in Z$,
for the function $y=\cos(2x- \frac{\pi}{6})$,
let $2x- \frac{\pi}{6}=k\pi \Rightarrow x= \frac{k\pi}{2}+ \frac{\pi}{12}$, where $k\in Z$, which represents the equation of its symmetry axis.
Among the four options, only $B$ fits.
Therefore, the answer is: $\boxed{B}$.
First, use the symmetry axis equation of $y=\cos x$, which is $x=k\pi$, and the idea of substituting the whole to find out the expression of all symmetry axis equations for $y=\cos(2x- \frac{\pi}{6})$, then check which answer fits the requirement.
This question mainly examines the symmetry of the cosine function and the application of the idea of substituting the whole. The key to solving such problems lies in remembering the properties of common functions and applying them, which is a basic question.