  We prove that a weak $\mathbb{Q}$-Fano $3$-fold with terminal singularities
has unobstructed deformations. By using this result and computing some
invariants of a terminal singularity, we provide two results on global
deformation of a weak $\mathbb{Q}$-Fano $3$-fold. We also treat a stacky proof
of the unobstructedness of deformations of a $\mathbb{Q}$-Fano $3$-fold.
