A closed simply-connected smooth manifold is projective plane like if its homology groups are the same as the homology groups of a projective plane over the complex numbers, the quaternions or the octonions. A smooth classification of projective-plane-like manifolds in dimension>4 was obtained by Kramer and Stolz in 2007. In a joint work with WANG Wei we computed the mapping class group of these manifolds. In this talk I will give a brief report of this computation.