Grumio is an old aged servant. He works for Petrucchio, who is a fortune seeker, as a servant. He travels with him from Verona to Padua in his search for fortune and power. He is also good with the puns and knows how to take advantage of those who are inferior to him in the house; this lets us see that Grumio is not as dumb as he plays. He knows perfectly when he is in a position of power and knows how to make the most of it. All in all as with most of Shakespeare’s fools, Grumio’s character is absolutely mysterious and ambiguous. There are reasons to think that he is just an amicably, loyal and funny fool. But there are reasons as well to think that his dumbness is a mask to hide his wit and a weapon to manipulate and handle others.
The Taming of the Shrew - Grumio and Curtis