Let a conducting solid sphere have a charge Q on its surface.so what is the potential at the centre.

See, the electric field inside the conducting sphere is zero because no charge resides inside its surface.
So, by the expression, E = -∂V/∂R 
V is constant since E is zero.
Thus, it will have the same value as it has on the surface i.e., V_center = V_surface
Hence, V_center = kQ/R  [where k = 1/4piE  and R is the radii of the sphere]