This talk is concerned with the existence and stability of travelling wave solutions of the following S-K-T competition model with cross-diffusion {ut =(c)2[(1 + β1u + γ1v)u]xx + (a1-b1u-c1v)uvt =[(1 +β2v+γ2u)v]xx+(a2-b2u-c2v)v (1)here (e) > 0,βi,γi ≥ 0,and ai,bi,ci > O,i =1,2.For small (e) > 0 and large Υ2 > 0,by geometric singular perturbation method,we can prove that there exist travelling waves connecting (0,a2/c2) and (a1/b1,O)with unique slow speed and the travelling waves have fast-slow structure.Further by topological index method and detailed spectral analysis,the travelling waves with transition layers are proved to be locally asymptotically stable.