newtonian mechanics - Force required to lift a block

Let us consider block of mass $m$ hanging by rope with force $T$. When no other horizontal and vertical forces are acting on a block, the block is at equilibrium if

$$T=mg.$$ And if the rope is pulled up a distance $h$, $$\text{work done}=mgh$$

Don't we need more force to move the block upward? If we just use $T$, the body will be in equilibrium. Don't we need more force to lift the block?