For a class of coupled KdV equations,the theory and method of planar dynamical system were applied to qualitatively analyse the dynamical system which the equation corresponds to.It is concluded that the equation has a unique bell profile solitary wave solution and infinite number of periodic wave solutions.The exact expressions of the bell solitary wave solution and the periodic solutions were provided by using the methods of undetermined coefficients and first integral respectively,and the positions of their orbits on the global phase portrait were pointed out.The relation between the solitary wave solution and the periodic wave solutions was discussed.Finally,3dimensional figures were presented to illustrate the evolution process of Jacobi elliptic functional periodic wave solution to bell solitary wave solution when the modulus tends to be 1.