In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$ hetaomega$ for a certain scalar $ heta$$ eq$c/2 and $ heta$$ eq$c/4 (4n-1)/(2n-1), where $omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).