In Mechanics, Sign (+ or -) is given to indicate direction. So, depending upon which direction you consider as positive, the initial velocity may be positive or negative.
To solve a problem, we take a convenient direction as positive and the direction opposite to it as negative.
In the case of vertical motion we may take the upward direction as positive and the downward direction as negative. So, if a stone is thrown vertically upwards, the initial velocity is TAKEN positive and if the stone is thrown downwards from a height, the initial velocity is taken as negative.