This is actually somewhat of a complicated topic. The overwhelming expectation is that anti-matter has the same inertial and gravitational mass as ordinary matter does. However, there are some intriguing possibilities for matter that doesn't.
Consider what happens if an object has "negative mass" though. It would be repelled by ordinary matter. OK, simple enough though, right. But then what happens? Well, F = ma right? So the repulsive force would repel ordinary matter, but it would result in an attractive acceleration of the negative mass. Now, if it turned out that gravitational and inertial mass could be different, that would be an incredible result as well.
(only a very rough grounding in particle physics here)
it offers an explanation for the abundance of matter - if large enough quantities of matter and anti-matter are created, and can gain enough separation, then although the attractive forces of the electromagnetic attraction are strong, the result of gravity repulsing opposite matter types would separate them. so matter/anti-matter creation would be symmetric, but all the anti matter would be beyond the edge of the observable universe.
lets just hope the LHC doesn't create a mini black hole which eats up the planet, before we find out..!
To further venture down the rabbit hole: it's unlikely that anti-matter actually has negative inertial mass though. Since that would result in an electrostatic repulsion from normal matter (which would, for example, prevent an anti-proton from annihilating with a nucleus). The observational evidence is pretty strong that anti-matter has at least a positive inertial mass. There is a remote possibility that inertial and gravitational masses can be different, which would be a very unexpected result.
Consider what happens if an object has "negative mass" though. It would be repelled by ordinary matter. OK, simple enough though, right. But then what happens? Well, F = ma right? So the repulsive force would repel ordinary matter, but it would result in an attractive acceleration of the negative mass. Now, if it turned out that gravitational and inertial mass could be different, that would be an incredible result as well.