The excitation of Alvén waves by high-energy ions in a Tokamak is investigated on the basis of the Vlasov equation, thus taking account of the finite gyro-radius and the finite orbit size of the ions. It is found that (i) The, growth rate of instability due to the spatial inhomogeneity of trapped fast ions is reduced for short wave perturbations (k±ρ
α_??_1, where ρ
α is the gyro-radius of fast ions), and (ii) There appears an instability, not present in the drift approximation (k±ρ
α<<1), when the trapped fast ions are spatially homogeneous having a monoenergetic distribution. The growth rate is comparable to the corresponding one due to untrapped fast ions if the velocity of fast ions is not greater than the Alfven velocity.
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