If force F , velocity V and time T are taken as fundamental units, the dimensions of mass are

The force is equal to the mass and the acceleration of the body.

$F=ma=\frac{mv}{t}$

It can be dimensionally represented as

$F=M\times \frac{L}{T^2}=\frac{ML}{TT}$
$F=\frac{MV}{T}$

So, the dimension of the mass is
$\left[M\right]=\left[FT{V}^{-1}\right]$