The SI unit of acceleration is:

Acceleration is the rate at which a body's speed or velocity changes in relation to time. 

Acceleration is given by:

$acceleration=\frac{velocity}{time}=\frac{m{s}^{-1}}{s}=m{s}^{-2}$

By substituting the SI units, as shown above, we get the SI unit of acceleration to be $m{s}^{-2}$.